Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
357 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 357 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 22. #6908 | Q8 | semidirect |
| 55. #737 | Dic6 | semidirect |
| 56. C32×C9 | Dic6 | semidirect |
| 57. #733 | Dic6 | semidirect |
| 58. #732 | Dic6 | semidirect |
| 59. #731 | Dic6 | semidirect |
| 60. AΣL(1,𝔽27) | Dic6 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6908 | 2 |
| #11757648 | 2 |
| #10619965 | 3 |
| C3×#6226 | 3 |
| #733⋊Q8 | 3 |
| #10619666 | 3 |
| #10619663 | 3 |
| #10619660 | 3 |