Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
706 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 120 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. #10590263 | C2 | semidirect |
| 3. #10589410 | C2 | semidirect |
| 4. C3×#4544 | C2 | semidirect |
| 5. #10589090 | C2 | semidirect |
| 15. C4⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 16. C3×C4⋊(C3⋊C8) | C22 | semidirect |
| 28. #4544 | D3 | semidirect |
| 70. C4⋊(C3⋊C8) | C2×D3 | semidirect |
| 266. C32 | #1555 | semidirect |
| 316. C3 | #68387 | semidirect |
| 317. C3 | #71760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D3×#127 | 2 |
| #10590263 | 2 |
| #10589410 | 2 |
| C3×#4544 | 2 |
| #10589090 | 2 |
| #71760 | 3 |
| #68387 | 3 |