Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
678 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#3746 | C2 | semidirect |
| 3. C2×#63654 | C2 | semidirect |
| 4. #10589415 | C2 | semidirect |
| 5. #10589358 | C2 | semidirect |
| 39. #3746 | D4 | semidirect |
| 98. C22×C32 | SD32 | semidirect |
| 161. C22×C3 | #827 | semidirect |
| 168. C32 | #2185 | semidirect |
| 196. C22 | #63654 | semidirect |
| 203. C3 | #71077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3746 | 2 |
| C32×#466 | 2 |
| C2×#63654 | 2 |
| #10589415 | 2 |
| #10589358 | 2 |
| #71077 | 3 |