Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
375 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 375 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 36. #3746 | C8 | semidirect |
| 198. C32 | #1579 | semidirect |
| 228. C3 | #68084 | semidirect |
| 229. C3 | #68517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3746 | 2 |
| #10590254 | 2 |
| C3×#4457 | 2 |
| C3×#4455 | 2 |
| #10589085 | 2 |
| #68517 | 3 |
| #68084 | 3 |