Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
465 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 465 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10594692 | C2 | semidirect |
| 2. C2×#63654 | C2 | semidirect |
| 3. C3×#5160 | C2 | semidirect |
| 4. C3×#5147 | C2 | semidirect |
| 5. #10589131 | C2 | semidirect |
| 6. #10589120 | C2 | semidirect |
| 7. #10589111 | C2 | semidirect |
| 31. #5160 | D3 | semidirect |
| 35. #5147 | D3 | semidirect |
| 340. C32 | #2193 | semidirect |
| 388. C3 | #71095 | semidirect |
| 389. C3 | #71518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10594692 | 2 |
| C2×#63654 | 2 |
| C3×#5160 | 2 |
| C3×#5147 | 2 |
| #10589131 | 2 |
| #10589120 | 2 |
| #10589111 | 2 |
| #71518 | 3 |
| #71095 | 3 |