Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
792 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 225 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. C2×C32×#108 | C2 | semidirect |
| 4. C2×#63644 | C2 | semidirect |
| 5. #10589420 | C2 | semidirect |
| 13. #64110 | C4 | semidirect |
| 22. C2×C3×#108 | D3 | semidirect |
| 89. C2×#108 | C3⋊D3 | semidirect |
| 207. C32 | #1815 | semidirect |
| 248. C3 | #70720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64110 | 2 |
| C2×C32×#108 | 2 |
| #10592832 | 2 |
| C2×#63644 | 2 |
| #10589420 | 2 |
| #70720 | 3 |