Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
152 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 72 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. C3×C7×Dic91 | C3 | semidirect |
| 3. ΓL(1,𝔽8)×Dic91 | C3 | direct (N × H) |
| 4. C3×C7×C13×ΓL(1,𝔽8) | C4 | semidirect |
| 9. C7×Dic91 | C32 | semidirect |
| 10. C3×C72×C13 | C3×C4 | semidirect |
| 11. C7×C13×ΓL(1,𝔽8) | C3×C4 | semidirect |
| 17. C3×Dic91 | ΓL(1,𝔽8) | direct (N × H) |
| 22. C3×C13×ΓL(1,𝔽8) | Dic7 | semidirect |
| 23. C72×C13 | C32×C4 | semidirect |
| 32. C3×C7×ΓL(1,𝔽8) | Dic13 | semidirect |
| 33. Dic91 | C3×ΓL(1,𝔽8) | direct (N × H) |
| 39. C3×C7×C13 | C4×ΓL(1,𝔽8) | semidirect |
| 40. C3×C7×C13 | C3×Dic7 | semidirect |
| 41. C13×ΓL(1,𝔽8) | C3×Dic7 | semidirect |
| 51. C3×C72 | C3×Dic13 | semidirect |
| 52. C7×ΓL(1,𝔽8) | C3×Dic13 | semidirect |
| 58. C7×C13 | C3×C4×ΓL(1,𝔽8) | semidirect |
| 59. C7×C13 | C32×Dic7 | semidirect |
| 67. C3×ΓL(1,𝔽8) | Dic91 | direct (N × H) |
| 69. C72 | C32×Dic13 | semidirect |
| 76. C3×C13 | ΓL(1,𝔽8)×Dic7 | semidirect |
| 83. C3×C7 | ΓL(1,𝔽8)×Dic13 | semidirect |
| 84. C3×C7 | C3×Dic91 | semidirect |
| 85. ΓL(1,𝔽8) | C3×Dic91 | direct (N × H) |
| 90. C13 | C3×ΓL(1,𝔽8)×Dic7 | semidirect |
| 95. C7 | C3×ΓL(1,𝔽8)×Dic13 | semidirect |
| 96. C7 | C32×Dic91 | semidirect |
| 101. C3 | ΓL(1,𝔽8)×Dic91 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×C13×ΓL(1,𝔽8) | 2 |
| C3×C7×Dic91 | 3 |
| ΓL(1,𝔽8)×Dic91 | 3 |
| C32×Dic91 | 7 |
| C3×ΓL(1,𝔽8)×Dic13 | 7 |
| C3×ΓL(1,𝔽8)×Dic7 | 13 |