Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
317 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 317 conjugacy classes of subgroups — too many to draw. Only its 88 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. #10590891 | C2 | semidirect |
| 5. #10589140 | C2 | semidirect |
| 6. #10589139 | C2 | semidirect |
| 7. Dic3⋊(C3⋊C16) | C2 | semidirect |
| 40. C32×D8 | Q8 | semidirect |
| 109. C3×D8 | Dic6 | semidirect |
| 110. C3×D8 | Dic6 | semidirect |
| 199. D8 | #627 | semidirect |
| 239. C32 | #2224 | semidirect |
| 278. C3 | #69178 | semidirect |
| 279. C3 | #70886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Dic3×D8 | 2 |
| #10590891 | 2 |
| #10589428 | 2 |
| C3×#4562 | 2 |
| #10589140 | 2 |
| #10589139 | 2 |
| Dic3⋊(C3⋊C16) | 2 |
| #70886 | 3 |
| #69178 | 3 |