Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1089 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 1089 conjugacy classes of subgroups — too many to draw. Only its 240 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 |
|---|---|---|
| 3. C3×#5184 | C2 | semidirect |
| 5. #10591541 | C2 | semidirect |
| 6. #10590810 | C2 | semidirect |
| 13. Q16×C3⋊D3 | C4 | semidirect |
| 34. #5184 | D3 | semidirect |
| 51. C32×Q16 | C2×C4 | semidirect |
| 53. #3756 | C2×C4 | semidirect |
| 55. #3746 | C2×C4 | semidirect |
| 147. C3×Q16 | C4×D3 | semidirect |
| 245. C3⋊D3 | #441 | semidirect |
| 257. Q16 | #624 | semidirect |
| 291. C32 | C2×#441 | semidirect |
| 329. C3 | D3×#441 | 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 |
| Q8×#624 | 2 |
| C3×#5184 | 2 |
| #10591552 | 2 |
| #10591541 | 2 |
| #10590810 | 2 |
| #10590685 | 2 |
| #10590668 | 2 |
| D3×#441 | 3 |