Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
152 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 60 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. C7×#11763964 | C3 | direct (N × H) |
| 4. C3×C7×#63271 | C4 | semidirect |
| 7. C3×#11763964 | C7 | direct (N × H) |
| 9. C7×Dic91 | C32 | semidirect |
| 10. C3×C72×C13 | C3×C4 | semidirect |
| 11. C7×#63271 | C3×C4 | semidirect |
| 16. C3×Dic91 | C3×C7 | semidirect |
| 18. #11763964 | C3×C7 | direct (N × H) |
| 21. C3×#63271 | C4×C7 | semidirect |
| 23. C72×C13 | C32×C4 | semidirect |
| 33. Dic91 | C32×C7 | semidirect |
| 38. C3×C7×C13 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 39. C3×C7×C13 | C3×C4×C7 | semidirect |
| 40. #63271 | C3×C4×C7 | semidirect |
| 51. C3×C72 | Dic13⋊C3 | semidirect |
| 58. C7×C13 | C3×ΓL(1,𝔽8)⋊C4 | semidirect |
| 59. C7×C13 | C32×C4×C7 | semidirect |
| 69. C72 | C3×Dic13⋊C3 | semidirect |
| 75. C3×C13 | C7×ΓL(1,𝔽8)⋊C4 | semidirect |
| 83. C3×C7 | C7×Dic13⋊C3 | semidirect |
| 84. C3×C7 | #11763964 | direct (N × H) |
| 90. C13 | C3×C7×ΓL(1,𝔽8)⋊C4 | semidirect |
| 95. C7 | C3×C7×Dic13⋊C3 | semidirect |
| 96. C7 | C3×#11763964 | direct (N × H) |
| 101. C3 | C7×#11763964 | 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×#63271 | 2 |
| C3×C7×Dic91 | 3 |
| C7×#11763964 | 3 |
| C3×#11763964 | 7 |
| C3×C7×Dic13⋊C3 | 7 |
| C3×C7×ΓL(1,𝔽8)⋊C4 | 13 |