Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1176 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 1176 conjugacy classes of subgroups — too many to draw. Only its 241 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 |
|---|---|---|
| 2. C22×#3746 | C2 | semidirect |
| 4. C2×#63643 | C2 | semidirect |
| 5. #10589417 | C2 | semidirect |
| 67. C23×C32 | Q16 | semidirect |
| 152. C23×C3 | Dic12 | semidirect |
| 221. C32 | #2001 | semidirect |
| 226. C23 | #3746 | semidirect |
| 271. C3 | #69964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64133 | 2 |
| C22×#3746 | 2 |
| C2×C32×C22⋊C8 | 2 |
| C2×#63643 | 2 |
| #10589417 | 2 |
| #69964 | 3 |