Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
333 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 333 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. #10592573 | C2 | semidirect |
| 4. C3×#4489 | C2 | semidirect |
| 5. #10589139 | C2 | semidirect |
| 6. #10589133 | C2 | semidirect |
| 35. #4489 | D3 | semidirect |
| 47. C3×D24 | Q8 | semidirect |
| 132. D24 | Dic6 | semidirect |
| 244. C32 | #2224 | semidirect |
| 282. C3 | #69178 | semidirect |
| 283. C3 | #69333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592573 | 2 |
| #10590777 | 2 |
| C3×#4491 | 2 |
| C3×#4489 | 2 |
| #10589139 | 2 |
| #10589133 | 2 |
| #10589115 | 2 |
| #69333 | 3 |
| #69178 | 3 |