Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
248 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D21⋊D91 |
| commutator, cosocle, hypocenter | C3×C72×C13 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C13 | C22 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C7⋊D91 | C2 | semidirect |
| 2. C3×C7×C13×D21 | C2 | semidirect |
| 3. C3×C7×D273 | C2 | semidirect |
| 4. D21⋊D91 | C3 | direct (N × H) |
| 6. C32×C72×C13 | C22 | semidirect |
| 7. C7×D273 | C2×C3 | semidirect |
| 8. C7×C13×D21 | C2×C3 | semidirect |
| 10. C3×C7⋊D91 | D3 | semidirect |
| 11. C3×C7⋊D91 | C2×C3 | semidirect |
| 18. C3×C72×C13 | C2×D3 | semidirect |
| 19. C3×C72×C13 | C22×C3 | semidirect |
| 21. C3×D273 | D7 | semidirect |
| 22. C3×C13×D21 | D7 | semidirect |
| 28. C7⋊D91 | C3×D3 | semidirect |
| 36. C3×C7×D21 | D13 | semidirect |
| 39. C32×C7×C13 | C2×D7 | semidirect |
| 40. C32×C7×C13 | C2×D7 | semidirect |
| 41. C72×C13 | C2×C3×D3 | semidirect |
| 45. D273 | C3×D7 | semidirect |
| 46. C13×D21 | C3×D7 | semidirect |
| 62. C32×C72 | C2×D13 | semidirect |
| 66. C7×D21 | C3×D13 | semidirect |
| 77. C3×C7×C13 | D3×D7 | semidirect |
| 78. C3×C7×C13 | D3×D7 | semidirect |
| 79. C3×C7×C13 | C2×C3×D7 | semidirect |
| 80. C3×C7×C13 | C2×C3×D7 | semidirect |
| 97. C3×C72 | D3×D13 | semidirect |
| 98. C3×C72 | C2×C3×D13 | semidirect |
| 100. C3×D21 | D91 | semidirect |
| 106. C32×C13 | D72 | semidirect |
| 111. C7×C13 | C3×D3×D7 | semidirect |
| 112. C7×C13 | C3×D3×D7 | semidirect |
| 125. C32×C7 | D7×D13 | semidirect |
| 126. C32×C7 | C2×D91 | semidirect |
| 128. C72 | C3×D3×D13 | semidirect |
| 132. D21 | C3×D91 | semidirect |
| 147. C3×C13 | C3×D72 | semidirect |
| 148. C3×C13 | D21⋊D7 | semidirect |
| 160. C3×C7 | C3×D7×D13 | semidirect |
| 161. C3×C7 | D3×D91 | semidirect |
| 162. C3×C7 | D21⋊D13 | semidirect |
| 163. C3×C7 | C2×C3×D91 | semidirect |
| 174. C13 | C3×D21⋊D7 | semidirect |
| 177. C32 | D7×D91 | semidirect |
| 179. C7 | C3×D3×D91 | semidirect |
| 180. C7 | C3×D21⋊D13 | semidirect |
| 190. C3 | C3×D7×D91 | semidirect |
| 191. C3 | D21⋊D91 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C7⋊D91 | 2 |
| C3×C7×C13×D21 | 2 |
| C3×C7×D273 | 2 |
| D21⋊D91 | 3 |
| C3×D7×D91 | 3 |
| C3×D21⋊D13 | 7 |
| C3×D3×D91 | 7 |
| C3×D21⋊D7 | 13 |