Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1422 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 263 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×#3744 | C2 | semidirect |
| 3. C2×#63648 | C2 | semidirect |
| 4. #10592628 | C2 | semidirect |
| 5. C32×#336 | C2 | semidirect |
| 23. C3×#336 | D3 | semidirect |
| 41. C2×#634 | D4 | semidirect |
| 44. C2×C32×C8 | D4 | semidirect |
| 69. C2×C32×C4 | SD16 | semidirect |
| 91. #336 | C3⋊D3 | semidirect |
| 112. C2×C3×C8 | D12 | semidirect |
| 151. C2×C3×C4 | #204 | semidirect |
| 196. C2×C8 | C4⋊(C3⋊D3) | semidirect |
| 214. C32 | #2014 | semidirect |
| 235. C2×C4 | #3744 | semidirect |
| 262. C3 | #68676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3744 | 2 |
| C2×#64083 | 2 |
| C2×#63648 | 2 |
| #10592628 | 2 |
| C32×#336 | 2 |
| #68676 | 3 |