Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
552 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 249 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 |
|---|---|---|
| 12. C32×#108 | C4 | semidirect |
| 46. C3×#108 | Dic3 | semidirect |
| 104. #108 | C3⋊Dic3 | semidirect |
| 150. C32 | #1953 | semidirect |
| 177. C3 | #70707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#108 | 2 |
| #10592824 | 2 |
| C2×#63646 | 2 |
| #10592800 | 2 |
| #10589425 | 2 |
| #70707 | 3 |