Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
312 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#63628 | C2 | semidirect |
| 3. C32×M64 | C2 | semidirect |
| 4. #10589316 | C2 | semidirect |
| 5. #10589315 | C2 | semidirect |
| 18. C3×M64 | D3 | semidirect |
| 55. M64 | C3⋊D3 | semidirect |
| 110. C32 | #2264 | semidirect |
| 130. C3 | #69374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63628 | 2 |
| #10592603 | 2 |
| C32×M64 | 2 |
| #10589316 | 2 |
| #10589315 | 2 |
| #69374 | 3 |