Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1332 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1332 conjugacy classes of subgroups — too many to draw. Only its 191 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. #10595992 | C2 | semidirect |
| 3. C32×#418 | C2 | semidirect |
| 4. #10592914 | C2 | semidirect |
| 5. C2×#63650 | C2 | semidirect |
| 6. #10589421 | C2 | semidirect |
| 7. #10589398 | C2 | semidirect |
| 15. #64149 | C4 | semidirect |
| 27. C3×#418 | D3 | semidirect |
| 39. C2×C32×D4 | C2×C4 | semidirect |
| 54. C32×C4⋊C4 | D4 | semidirect |
| 59. C4⋊(C3⋊Dic3) | D4 | semidirect |
| 62. C4×C3⋊Dic3 | C2×C4 | semidirect |
| 117. #418 | C3⋊D3 | semidirect |
| 128. C2×C3×D4 | C4×D3 | semidirect |
| 143. C3×C4⋊C4 | #67 | semidirect |
| 242. C2×D4 | C4×C3⋊D3 | semidirect |
| 253. C4⋊C4 | #638 | semidirect |
| 280. C32 | #1887 | semidirect |
| 337. C3 | #70323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64149 | 2 |
| #10595992 | 2 |
| C32×#418 | 2 |
| #10592914 | 2 |
| C2×#63650 | 2 |
| #10589421 | 2 |
| #10589398 | 2 |
| #70323 | 3 |