Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
368 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 88 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×#4831 | C2 | semidirect |
| 4. #10590301 | C2 | semidirect |
| 5. #10589348 | C2 | semidirect |
| 7. #10589099 | C2 | semidirect |
| 31. #4831 | D3 | semidirect |
| 113. C3×C3⋊C8 | SD16 | semidirect |
| 241. C3⋊C8 | #215 | semidirect |
| 296. C32 | #1686 | semidirect |
| 342. C3 | #68412 | semidirect |
| 343. C3 | #70958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4831 | 2 |
| #10590369 | 2 |
| #10590364 | 2 |
| #10590301 | 2 |
| #10589348 | 2 |
| C3×#4485 | 2 |
| #10589099 | 2 |
| #70958 | 3 |
| #68412 | 3 |