Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
305 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 305 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10590875 | C2 | semidirect |
| 3. C16×C3⋊Dic3 | C2 | semidirect |
| 5. C3×#4503 | C2 | semidirect |
| 6. #10589117 | C2 | semidirect |
| 30. #4503 | D3 | semidirect |
| 247. C32 | #2242 | semidirect |
| 285. C3 | #69184 | semidirect |
| 286. C3 | #69216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590875 | 2 |
| #10590869 | 2 |
| C16×C3⋊Dic3 | 2 |
| C3×#4509 | 2 |
| C3×#4503 | 2 |
| #10589117 | 2 |
| #10589114 | 2 |
| #69216 | 3 |
| #69184 | 3 |