Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1236 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1236 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×#3748 | C2 | semidirect |
| 3. C32×#380 | C2 | semidirect |
| 4. C2×#63636 | C2 | semidirect |
| 5. #10589395 | C2 | semidirect |
| 13. #64139 | C4 | semidirect |
| 23. C3×#380 | D3 | semidirect |
| 51. C2×C3⋊(C3⋊C8) | D4 | semidirect |
| 100. #380 | C3⋊D3 | semidirect |
| 247. C32 | #1895 | semidirect |
| 306. C3 | #69517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64139 | 2 |
| C22×#3748 | 2 |
| C32×#380 | 2 |
| C2×#63636 | 2 |
| #10589395 | 2 |
| #69517 | 3 |