Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
152 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 23 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, cosocle, hypocenter | C13×#3862 | C22×C3 |
| Fitting, socle | C72×C13 | C2×C3×D3 |
| LCS | G ▷ C13×#3862 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26039565 | C2 | semidirect |
| 2. C13×#64418⋊C3 | C2 | semidirect |
| 3. ΓL(1,𝔽8)2×D13 | C2 | semidirect |
| 4. D13×#64418 | C3 | semidirect |
| 6. C13×ΓL(1,𝔽8)2 | C22 | semidirect |
| 7. C13⋊#64418 | C2×C3 | semidirect |
| 8. C13×#64418 | C2×C3 | semidirect |
| 9. D13×#3862 | C2×C3 | semidirect |
| 10. D13×#3861 | D3 | semidirect |
| 15. C13×#3862 | C22×C3 | semidirect |
| 16. C13×#3861 | C2×D3 | semidirect |
| 22. C72×D13 | C3×D3 | semidirect |
| 27. #64418⋊C3 | D13 | direct (N × H) |
| 29. C72×C13 | C2×C3×D3 | semidirect |
| 43. ΓL(1,𝔽8)2 | C2×D13 | semidirect |
| 52. #64418 | C3×D13 | semidirect |
| 72. #3862 | C2×C3×D13 | semidirect |
| 73. #3861 | D3×D13 | semidirect |
| 94. C72 | C3×D3×D13 | semidirect |
| 113. D13 | #64418⋊C3 | direct (N × H) |
| 130. C13 | C2×#64418⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039565 | 2 |
| C13×#64418⋊C3 | 2 |
| ΓL(1,𝔽8)2×D13 | 2 |
| D13×#64418 | 3 |
| D13×#64423 | 3 |
| C2×#64418⋊C3 | 13 |
| C3×D3×D13 | 49 |