Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
720 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 131 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. #10592777 | C2 | semidirect |
| 3. #10592545 | C2 | semidirect |
| 4. #10592540 | C2 | semidirect |
| 5. C32×#332 | C2 | semidirect |
| 6. #10589349 | C2 | semidirect |
| 7. #10589349 | C2 | semidirect |
| 30. C3×#332 | D3 | semidirect |
| 106. #332 | C3⋊D3 | semidirect |
| 239. C32 | #1647 | semidirect |
| 287. C3 | #68436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596197 | 2 |
| #10592777 | 2 |
| #10592545 | 2 |
| #10592540 | 2 |
| C32×#332 | 2 |
| #10589349 | 2 |
| #68436 | 3 |