Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
152 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #26039565 |
| commutator, cosocle, hypocenter | C13×#3862 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C13 | C3×D3 |
| LCS | G ▷ C13×#3862 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×ΓL(1,𝔽8)2 | C2 | semidirect |
| 2. #26039565 | C2 | direct (N × H) |
| 3. C2×C13⋊#64418 | C3 | semidirect |
| 5. C13×ΓL(1,𝔽8)2 | C22 | semidirect |
| 6. C2×C13×#3862 | C2×C3 | semidirect |
| 7. C2×C13×#3861 | D3 | semidirect |
| 9. C13⋊#64418 | C2×C3 | semidirect |
| 12. C13×#3862 | C22×C3 | semidirect |
| 13. C13×#3861 | C2×D3 | semidirect |
| 17. C2×C72×C13 | C3×D3 | semidirect |
| 21. C2×ΓL(1,𝔽8)2 | D13 | semidirect |
| 24. C72×C13 | C2×C3×D3 | semidirect |
| 36. ΓL(1,𝔽8)2 | C2×D13 | semidirect |
| 39. C2×#3862 | C3×D13 | semidirect |
| 40. C2×#3861 | D39 | semidirect |
| 60. #3862 | C2×C3×D13 | semidirect |
| 61. #3861 | C2×D39 | semidirect |
| 65. C2×C72 | C3×D39 | semidirect |
| 79. C72 | C2×C3×D39 | semidirect |
| 94. C2×C13 | #64418⋊C3 | semidirect |
| 109. C13 | C2×#64418⋊C3 | semidirect |
| 126. C2 | #26039565 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×ΓL(1,𝔽8)2 | 2 |
| #26039565 | 2 |
| C2×C13⋊#64418 | 3 |
| C2×#16838460 | 3 |
| C2×#64418⋊C3 | 13 |
| C2×C3×D39 | 49 |