Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
180 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 44 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×#63540 | C2 | semidirect |
| 40. C22×C32 | C32 | semidirect |
| 76. C32 | C22⋊C32 | semidirect |
| 91. C22 | #63540 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C3⋊C16) | 2 |
| C2×#63540 | 2 |
| C22⋊C32 | 9 |