Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
309 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 309 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 1. #10590902 | C2 | semidirect |
| 3. #10589367 | C2 | semidirect |
| 5. C3×#4504 | C2 | semidirect |
| 6. #10589140 | C2 | semidirect |
| 29. #4504 | D3 | semidirect |
| 46. C3×D24 | Q8 | semidirect |
| 126. D24 | Dic6 | semidirect |
| 235. C32 | #2224 | semidirect |
| 273. C3 | #69178 | semidirect |
| 274. C3 | #69333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590902 | 2 |
| #10590777 | 2 |
| #10589367 | 2 |
| C3×#4509 | 2 |
| C3×#4504 | 2 |
| #10589140 | 2 |
| #10589114 | 2 |
| #69333 | 3 |
| #69178 | 3 |