Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
786 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 177 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 |
| 3. C2×#63651 | C2 | semidirect |
| 6. C2×#63643 | C2 | semidirect |
| 7. #10589420 | C2 | semidirect |
| 27. C2×C3×#108 | D3 | semidirect |
| 115. C2×#108 | C3⋊D3 | semidirect |
| 270. C32 | #2052 | semidirect |
| 322. C3 | #70716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64118 | 2 |
| C2×C32×#108 | 2 |
| C2×#63651 | 2 |
| #10592832 | 2 |
| #10592809 | 2 |
| C2×#63643 | 2 |
| #10589420 | 2 |
| #70716 | 3 |