Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
395 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 395 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 1. C3×#4848 | C2 | semidirect |
| 2. #10590364 | C2 | semidirect |
| 4. #10590259 | C2 | semidirect |
| 5. #10589346 | C2 | semidirect |
| 6. C3×#4485 | C2 | semidirect |
| 7. #10589090 | C2 | semidirect |
| 31. #4848 | D3 | semidirect |
| 36. #4485 | D3 | semidirect |
| 116. C3⋊(C3⋊C8) | SD16 | semidirect |
| 313. C32 | #1688 | semidirect |
| 366. C3 | #68413 | semidirect |
| 367. C3 | #71025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4848 | 2 |
| #10590364 | 2 |
| #10590352 | 2 |
| #10590259 | 2 |
| #10589346 | 2 |
| C3×#4485 | 2 |
| #10589090 | 2 |
| #71025 | 3 |
| #68413 | 3 |