Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
645 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 645 conjugacy classes of subgroups — too many to draw. Only its 124 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. C2×#63578 | C2 | semidirect |
| 3. #10591138 | C2 | semidirect |
| 5. C3×#4559 | C2 | semidirect |
| 12. #64116 | C4 | semidirect |
| 13. #64116 | C4 | semidirect |
| 30. #4559 | D3 | semidirect |
| 306. C32 | #1814 | semidirect |
| 354. C3 | #69032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64116 | 2 |
| C2×#63578 | 2 |
| #10591138 | 2 |
| #10591113 | 2 |
| C3×#4559 | 2 |
| #69032 | 3 |