Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
288 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 97 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. C32×#322 | C2 | semidirect |
| 3. #10589329 | C2 | semidirect |
| 13. C3×#322 | D3 | semidirect |
| 21. #3746 | C8 | semidirect |
| 22. #3745 | C8 | semidirect |
| 49. #322 | C3⋊D3 | semidirect |
| 108. C32 | #1336 | semidirect |
| 130. C3 | #67443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592399 | 2 |
| C32×#322 | 2 |
| #10589329 | 2 |
| #67443 | 3 |