Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
421 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 421 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 7. #71296 | C3 | direct (N × H) |
| 70. C3×C3⋊C8 | Q16 | semidirect |
| 144. C3⋊C8 | C3×Q16 | semidirect |
| 176. C32 | #1707 | semidirect |
| 203. C3 | #71296 | direct (N × H) |
| 204. C3 | C3×#1707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#494 | 2 |
| C3×#5093 | 2 |
| C3×#5080 | 2 |
| C3×#4682 | 2 |
| C3×C8×C3⋊C8 | 2 |
| C3×#1707 | 3 |
| #71296 | 3 |