Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
924 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 3. C2×C32×#101 | C2 | semidirect |
| 4. C2×#63663 | C2 | semidirect |
| 6. #10589425 | C2 | semidirect |
| 7. #10589422 | C2 | semidirect |
| 29. C2×C3×#101 | D3 | semidirect |
| 121. C2×#101 | C3⋊D3 | semidirect |
| 272. C32 | #1915 | semidirect |
| 320. C3 | #70124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596287 | 2 |
| #10596216 | 2 |
| C2×C32×#101 | 2 |
| C2×#63663 | 2 |
| #10592831 | 2 |
| #10589425 | 2 |
| #10589422 | 2 |
| #70124 | 3 |