Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
248 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C13 | C22×C3 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊#16838459 | C2 | semidirect |
| 2. C3×#16838449 | C2 | semidirect |
| 3. C13×D21⋊D7 | C3 | semidirect |
| 5. C3×#14274262 | C22 | semidirect |
| 6. C7×C13×D21 | C2×C3 | semidirect |
| 7. C3×C13×C7⋊D7 | C2×C3 | semidirect |
| 10. #16838449 | D3 | semidirect |
| 13. C3×C72×C13 | C22×C3 | semidirect |
| 15. #14274262 | C2×D3 | semidirect |
| 21. C13×C7⋊D7 | C3×D3 | semidirect |
| 29. C72×C13 | C2×C3×D3 | semidirect |
| 30. D21⋊D7 | C13⋊C3 | semidirect |
| 32. C13×D21 | AGL(1,𝔽7) | semidirect |
| 45. C7×D21 | C2×C13⋊C3 | semidirect |
| 46. C3×C7⋊D7 | C2×C13⋊C3 | semidirect |
| 51. C3×C7×C13 | C2×AGL(1,𝔽7) | semidirect |
| 66. C3×C72 | C22×C13⋊C3 | semidirect |
| 74. C7⋊D7 | D3×C13⋊C3 | semidirect |
| 77. C7×C13 | D3×AGL(1,𝔽7) | semidirect |
| 88. C72 | C2×D3×C13⋊C3 | semidirect |
| 89. D21 | #10587721 | semidirect |
| 99. C3×C13 | #64423⋊C2 | semidirect |
| 107. C3×C7 | C2×#10587721 | semidirect |
| 118. C13 | #13183634 | semidirect |
| 123. C7 | D3×#10587721 | semidirect |
| 132. C3 | #21439613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊#16838459 | 2 |
| C3×#16838449 | 2 |
| C13×D21⋊D7 | 3 |
| #21439613 | 3 |
| D3×#10587721 | 7 |
| #13183634 | 13 |