Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
184 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #13183625 |
| commutator, cosocle, hypocenter | C3×#3862 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C2×D3 |
| LCS | G ▷ C3×#3862 | |
| UCS | C1 ◁ C13 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×C3⋊#64418 | C2 | semidirect |
| 2. C3×C13×#64425 | C2 | semidirect |
| 5. C3×C13×#3862 | C22 | semidirect |
| 7. C3×C13×C7⋊D7 | D3 | semidirect |
| 9. C13×#64425 | D3 | semidirect |
| 11. C3×C72×C13 | C2×D3 | semidirect |
| 12. C13×#3862 | C2×D3 | semidirect |
| 13. #13183625 | C13 | direct (N × H) |
| 15. C13×C7⋊D7 | C3⋊D3 | semidirect |
| 18. C3×#64425 | C2×C13 | semidirect |
| 19. C3⋊#64418 | C2×C13 | semidirect |
| 21. C72×C13 | C2×C3⋊D3 | semidirect |
| 30. C3×#3862 | C22×C13 | semidirect |
| 33. C3×C7⋊D7 | D3×C13 | semidirect |
| 34. #64425 | D3×C13 | semidirect |
| 48. C3×C72 | C2×D3×C13 | semidirect |
| 49. #3862 | C2×D3×C13 | semidirect |
| 52. C7⋊D7 | C13×C3⋊D3 | semidirect |
| 63. C72 | C2×C13×C3⋊D3 | semidirect |
| 70. C3×C13 | #64418⋊C2 | semidirect |
| 84. C13 | #13183625 | direct (N × H) |
| 96. C3 | C13×#64418⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×C3⋊#64418 | 2 |
| C3×C13×#64425 | 2 |
| C13×D21⋊D7 | 3 |
| C13×#64418⋊C2 | 3 |
| #13183625 | 13 |
| C2×C13×C3⋊D3 | 49 |