Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1201 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 1201 conjugacy classes of subgroups — too many to draw. Only its 220 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×C3×#904 | C2 | semidirect |
| 2. #10595032 | C2 | semidirect |
| 3. C2×#63822 | C2 | semidirect |
| 4. C2×#63642 | C2 | semidirect |
| 5. #10590887 | C2 | semidirect |
| 6. #10590870 | C2 | semidirect |
| 29. C2×#904 | D3 | semidirect |
| 45. C2×C32×C8 | D4 | semidirect |
| 49. C2×C3⋊(C3⋊C8) | D4 | semidirect |
| 136. C2×C3×C8 | #67 | semidirect |
| 242. C2×C8 | #625 | semidirect |
| 268. C32 | #3150 | semidirect |
| 306. C3 | #83904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#904 | 2 |
| #10595032 | 2 |
| C2×#63822 | 2 |
| C2×#63642 | 2 |
| #10590887 | 2 |
| #10590870 | 2 |
| #83904 | 3 |