Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
559 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 559 conjugacy classes of subgroups — too many to draw. Only its 96 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. #10592769 | C2 | semidirect |
| 3. #10590365 | C2 | semidirect |
| 4. #10590301 | C2 | semidirect |
| 5. C3×#4544 | C2 | semidirect |
| 6. #10589083 | C2 | semidirect |
| 7. #10589080 | C2 | semidirect |
| 37. #4544 | D3 | semidirect |
| 130. C3×Dic6 | SD16 | semidirect |
| 293. Dic6 | #214 | semidirect |
| 373. C32 | #1642 | semidirect |
| 433. C3 | #68393 | semidirect |
| 434. C3 | #71921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5718 | 2 |
| #10592769 | 2 |
| #10590365 | 2 |
| #10590301 | 2 |
| C3×#4544 | 2 |
| #10589083 | 2 |
| #10589080 | 2 |
| #71921 | 3 |
| #68393 | 3 |