Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
518 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 19. C32×C42 | C8 | semidirect |
| 111. C42 | #622 | semidirect |
| 123. C32 | #1831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#622 | 2 |
| C42×C3⋊Dic3 | 2 |
| #10590207 | 2 |
| #1831 | 9 |