Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1794 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1794 conjugacy classes of subgroups — too many to draw. Only its 195 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. C2×C22⋊C4×C3⋊D3 | C2 | semidirect |
| 3. #10592654 | C2 | semidirect |
| 4. C2×#63633 | C2 | semidirect |
| 5. C2×#63633 | C2 | semidirect |
| 6. C32×#342 | C2 | semidirect |
| 7. #10589392 | C2 | semidirect |
| 11. C22×C4⋊(C3⋊D3) | C4 | semidirect |
| 20. C2×#3752 | C4 | semidirect |
| 33. C3×#342 | D3 | semidirect |
| 42. C23×C3⋊D3 | C2×C4 | semidirect |
| 48. C22×C32×C4 | C2×C4 | semidirect |
| 57. C22×C3⋊Dic3 | C2×C4 | semidirect |
| 68. C32×C22⋊C4 | D4 | semidirect |
| 72. #3757 | D4 | semidirect |
| 155. #342 | C3⋊D3 | semidirect |
| 169. C22×C3×C4 | C4×D3 | semidirect |
| 189. C3×C22⋊C4 | D12 | semidirect |
| 229. C2×C3⋊D3 | #99 | semidirect |
| 345. C22×C4 | C4×C3⋊D3 | semidirect |
| 359. C22⋊C4 | C4⋊(C3⋊D3) | semidirect |
| 398. C32 | #1898 | semidirect |
| 500. C3 | #68970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64091 | 2 |
| C2×C22⋊C4×C3⋊D3 | 2 |
| #10592654 | 2 |
| C2×#63633 | 2 |
| C32×#342 | 2 |
| #10589392 | 2 |
| #68970 | 3 |