Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
168 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 48 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. C4×C13⋊#3862 | C3 | semidirect |
| 3. C4×C13×#3861 | C3 | semidirect |
| 4. C4×C7×#63271 | C3 | semidirect |
| 5. C4×C7×#63270 | C3 | semidirect |
| 6. #3861⋊(C13⋊C3) | C4 | direct (N × H) |
| 13. C4×C72×C13 | C32 | semidirect |
| 14. C13⋊#3862 | C3×C4 | semidirect |
| 15. C13×#3861 | C3×C4 | semidirect |
| 16. C7×#63270 | C3×C4 | semidirect |
| 17. C7×#63271 | C3×C4 | semidirect |
| 23. C4×#63271 | ΓL(1,𝔽8) | semidirect |
| 25. C4×#63270 | ΓL(1,𝔽8) | semidirect |
| 34. C72×C13 | C32×C4 | semidirect |
| 36. C4×#3861 | C13⋊C3 | semidirect |
| 51. C4×C7×C13 | C3×ΓL(1,𝔽8) | semidirect |
| 52. C4×C7×C13 | C3×ΓL(1,𝔽8) | semidirect |
| 58. #63271 | C4×ΓL(1,𝔽8) | semidirect |
| 60. #63270 | C4×ΓL(1,𝔽8) | semidirect |
| 69. C4×C72 | C3×C13⋊C3 | semidirect |
| 78. #3861 | C4×C13⋊C3 | semidirect |
| 86. C7×C13 | C3×C4×ΓL(1,𝔽8) | semidirect |
| 87. C7×C13 | C3×C4×ΓL(1,𝔽8) | semidirect |
| 103. C4×C13 | ΓL(1,𝔽8)2 | semidirect |
| 104. C72 | C3×C4×C13⋊C3 | semidirect |
| 120. C4×C7 | ΓL(1,𝔽8)×C13⋊C3 | semidirect |
| 121. C4×C7 | ΓL(1,𝔽8)×C13⋊C3 | semidirect |
| 136. C13 | C4×ΓL(1,𝔽8)2 | semidirect |
| 143. C7 | C4×ΓL(1,𝔽8)×C13⋊C3 | semidirect |
| 144. C7 | C4×ΓL(1,𝔽8)×C13⋊C3 | semidirect |
| 149. C4 | #3861⋊(C13⋊C3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3861⋊(C13⋊C3) | 2 |
| C4×C13⋊#3862 | 3 |
| C4×C13×#3861 | 3 |
| C4×C7×#63271 | 3 |
| C4×C7×#63270 | 3 |
| C4×ΓL(1,𝔽8)×C13⋊C3 | 7 |
| C4×ΓL(1,𝔽8)2 | 13 |