Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
593 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 593 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 4. C3×#4564 | C2 | semidirect |
| 5. #10589119 | C2 | semidirect |
| 11. Q16×C3⋊D3 | C4 | semidirect |
| 24. #4564 | D3 | semidirect |
| 36. C32×Q16 | C2×C4 | semidirect |
| 41. #3746 | C2×C4 | semidirect |
| 110. C3×Q16 | C4×D3 | semidirect |
| 190. C3⋊D3 | #358 | semidirect |
| 203. Q16 | #624 | semidirect |
| 231. C32 | C2×#358 | semidirect |
| 269. C3 | D3×#358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×C3⋊D3 | 2 |
| #10590687 | 2 |
| C2×#63542 | 2 |
| C3×#4564 | 2 |
| #10589119 | 2 |
| D3×#358 | 3 |