Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
492 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 169 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 |
|---|---|---|
| 8. C32×C4⋊C8 | C4 | semidirect |
| 14. #63630 | C4 | semidirect |
| 34. C3×C4⋊C8 | Dic3 | semidirect |
| 88. C4⋊C8 | C3⋊Dic3 | semidirect |
| 139. C32 | #1285 | semidirect |
| 173. C3 | #67750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#432 | 2 |
| C4×C4⋊(C3⋊Dic3) | 2 |
| #10592625 | 2 |
| #67750 | 3 |