Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
341 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 90 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. #10592399 | C2 | semidirect |
| 2. C3×#4700 | C2 | semidirect |
| 4. C3×#4461 | C2 | semidirect |
| 5. #10589143 | C2 | semidirect |
| 6. #10589122 | C2 | semidirect |
| 7. #10589121 | C2 | semidirect |
| 21. #63551 | C4 | semidirect |
| 22. #63549 | C4 | semidirect |
| 23. #63548 | C4 | semidirect |
| 24. #63546 | C4 | semidirect |
| 31. #4700 | D3 | semidirect |
| 39. #4461 | D3 | semidirect |
| 281. C32 | #2179 | semidirect |
| 318. C3 | #69085 | semidirect |
| 319. C3 | #70922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592399 | 2 |
| C3×#4700 | 2 |
| #10590632 | 2 |
| C3×#4461 | 2 |
| #10589143 | 2 |
| #10589122 | 2 |
| #10589121 | 2 |
| #70922 | 3 |
| #69085 | 3 |