Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
396 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 2. #10590369 | C2 | semidirect |
| 3. #10590337 | C2 | semidirect |
| 4. #10590272 | C2 | semidirect |
| 5. #10589352 | C2 | semidirect |
| 6. C3×#4479 | C2 | semidirect |
| 7. #10589090 | C2 | semidirect |
| 39. #4479 | D3 | semidirect |
| 116. C3×C3⋊C8 | D8 | semidirect |
| 252. C3⋊C8 | D24 | semidirect |
| 313. C32 | #1685 | semidirect |
| 365. C3 | #68582 | semidirect |
| 366. C3 | #71008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4843 | 2 |
| #10590369 | 2 |
| #10590337 | 2 |
| #10590272 | 2 |
| #10589352 | 2 |
| C3×#4479 | 2 |
| #10589090 | 2 |
| #71008 | 3 |
| #68582 | 3 |