Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
528 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 149 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. C32×C8×D4 | C2 | semidirect |
| 3. #10592707 | C2 | semidirect |
| 4. #10592393 | C2 | semidirect |
| 5. #10589351 | C2 | semidirect |
| 6. #10589347 | C2 | semidirect |
| 7. #10589323 | C2 | semidirect |
| 24. C3×C8×D4 | D3 | semidirect |
| 90. C8×D4 | C3⋊D3 | semidirect |
| 200. C32 | #1677 | semidirect |
| 242. C3 | #70848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C8×D4 | 2 |
| #10592714 | 2 |
| #10592707 | 2 |
| #10592393 | 2 |
| #10589351 | 2 |
| #10589347 | 2 |
| #10589323 | 2 |
| #70848 | 3 |