Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
168 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
| 23. C3×C13×ΓL(1,𝔽8) | Dic7 | semidirect |
| 24. C72×C13 | C32×C4 | semidirect |
| 33. C3×C7×ΓL(1,𝔽8) | Dic13 | semidirect |
| 41. C3×C7×C13 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 42. C3×C7×C13 | C3×Dic7 | semidirect |
| 43. C13×ΓL(1,𝔽8) | C3×Dic7 | semidirect |
| 53. C3×C72 | C3×Dic13 | semidirect |
| 54. C7×ΓL(1,𝔽8) | C3×Dic13 | semidirect |
| 60. C7×C13 | C3×ΓL(1,𝔽8)⋊C4 | semidirect |
| 61. C7×C13 | C32×Dic7 | semidirect |
| 70. C3×ΓL(1,𝔽8) | Dic91 | semidirect |
| 72. C72 | C32×Dic13 | semidirect |
| 79. C3×C13 | ΓL(1,𝔽8)⋊Dic7 | semidirect |
| 87. C3×C7 | ΓL(1,𝔽8)⋊Dic13 | semidirect |
| 88. C3×C7 | C3×Dic91 | semidirect |
| 89. ΓL(1,𝔽8) | C3×Dic91 | semidirect |
| 94. C13 | C3×ΓL(1,𝔽8)⋊Dic7 | semidirect |
| 99. C7 | C3×ΓL(1,𝔽8)⋊Dic13 | semidirect |
| 100. C7 | C32×Dic91 | semidirect |
| 105. 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 |