Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
480 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 4. #10592380 | C2 | semidirect |
| 5. C32×#335 | C2 | semidirect |
| 6. #10589352 | C2 | semidirect |
| 7. #10589347 | C2 | semidirect |
| 28. C3×#335 | D3 | semidirect |
| 87. #335 | C3⋊D3 | semidirect |
| 186. C32 | #1683 | semidirect |
| 222. C3 | #68581 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592545 | 2 |
| #10592541 | 2 |
| C8×C4⋊(C3⋊D3) | 2 |
| #10592380 | 2 |
| C32×#335 | 2 |
| #10589352 | 2 |
| #10589347 | 2 |
| #68581 | 3 |