Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
924 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 3. C2×#63651 | C2 | semidirect |
| 4. C2×#63651 | C2 | semidirect |
| 6. C32×#344 | C2 | semidirect |
| 7. #10589399 | C2 | semidirect |
| 32. C3×#344 | D3 | semidirect |
| 123. #344 | C3⋊D3 | semidirect |
| 272. C32 | #1915 | semidirect |
| 320. C3 | #69041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596216 | 2 |
| #10595997 | 2 |
| C2×#63651 | 2 |
| #10592831 | 2 |
| C32×#344 | 2 |
| #10589399 | 2 |
| #69041 | 3 |