Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
305 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 305 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10590873 | C2 | semidirect |
| 5. #10589141 | C2 | semidirect |
| 6. #10589140 | C2 | semidirect |
| 7. Dic3⋊(C3⋊C16) | C2 | semidirect |
| 236. C32 | #2228 | semidirect |
| 274. C3 | #69181 | semidirect |
| 275. C3 | #70888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Dic3×D8 | 2 |
| #10590873 | 2 |
| #10589428 | 2 |
| C3×#4562 | 2 |
| #10589141 | 2 |
| #10589140 | 2 |
| Dic3⋊(C3⋊C16) | 2 |
| #70888 | 3 |
| #69181 | 3 |