Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
216 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C7×Dic91 | C3 | semidirect |
| 3. C7×#11763955 | C3 | direct (N × H) |
| 4. C3×C72×C13⋊C3 | C4 | semidirect |
| 7. C3×#11763955 | C7 | direct (N × H) |
| 9. C7×Dic91 | C32 | semidirect |
| 10. C3×C72×C13 | C3×C4 | semidirect |
| 11. C72×C13⋊C3 | C3×C4 | semidirect |
| 17. C3×Dic91 | C3×C7 | semidirect |
| 19. #11763955 | C3×C7 | direct (N × H) |
| 23. C3×C7×C13⋊C3 | Dic7 | semidirect |
| 24. C3×C7×C13⋊C3 | C4×C7 | semidirect |
| 25. C72×C13 | C32×C4 | semidirect |
| 36. Dic91 | C32×C7 | semidirect |
| 41. C3×C7×C13 | C3×Dic7 | semidirect |
| 42. C3×C7×C13 | C3×C4×C7 | semidirect |
| 44. C7×C13⋊C3 | C3×Dic7 | semidirect |
| 45. C7×C13⋊C3 | C3×C4×C7 | semidirect |
| 56. C3×C72 | Dic13⋊C3 | semidirect |
| 60. C3×C13⋊C3 | C7×Dic7 | semidirect |
| 63. C7×C13 | C32×Dic7 | semidirect |
| 64. C7×C13 | C32×C4×C7 | semidirect |
| 75. C72 | C3×Dic13⋊C3 | semidirect |
| 82. C3×C13 | C3×C7×Dic7 | semidirect |
| 83. C13⋊C3 | C3×C7×Dic7 | semidirect |
| 92. C3×C7 | C7×Dic13⋊C3 | semidirect |
| 93. C3×C7 | #11763955 | direct (N × H) |
| 98. C13 | C32×C7×Dic7 | semidirect |
| 103. C7 | C3×C7×Dic13⋊C3 | semidirect |
| 104. C7 | C3×#11763955 | direct (N × H) |
| 109. C3 | C7×#11763955 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C72×C13⋊C3 | 2 |
| C3×C7×Dic91 | 3 |
| C7×#11763955 | 3 |
| C3×#11763955 | 7 |
| C3×C7×Dic13⋊C3 | 7 |
| C32×C7×Dic7 | 13 |