Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
771 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 771 conjugacy classes of subgroups — too many to draw. Only its 182 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×#5584 | C2 | semidirect |
| 2. Q8×C3⋊(C3⋊C8) | C2 | semidirect |
| 3. #10590387 | C2 | semidirect |
| 4. C4×#3718 | C2 | semidirect |
| 5. #10590363 | C2 | semidirect |
| 8. #10590267 | C2 | semidirect |
| 30. #5584 | D3 | semidirect |
| 283. C32 | #3393 | semidirect |
| 322. C3 | #83670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5584 | 2 |
| Q8×C3⋊(C3⋊C8) | 2 |
| #10590387 | 2 |
| C4×#3718 | 2 |
| #10590363 | 2 |
| #10590353 | 2 |
| C4×#3713 | 2 |
| #10590267 | 2 |
| #83670 | 3 |