Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
474 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×C32×Q32 | C2 | semidirect |
| 3. Q16×C3⋊Dic3 | C2 | semidirect |
| 5. #10589430 | C2 | semidirect |
| 7. #10589367 | C2 | semidirect |
| 22. C2×C3×Q32 | D3 | semidirect |
| 79. C2×Q32 | C3⋊D3 | semidirect |
| 181. C32 | #2211 | semidirect |
| 213. C3 | #71498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q32 | 2 |
| #10592890 | 2 |
| Q16×C3⋊Dic3 | 2 |
| C2×#63655 | 2 |
| #10589430 | 2 |
| #10589375 | 2 |
| #10589367 | 2 |
| #71498 | 3 |