Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
409 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 409 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. #70533 | C3 | direct (N × H) |
| 204. C32 | #2090 | semidirect |
| 234. C3 | #70533 | direct (N × H) |
| 235. C3 | C3×#2090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#424 | 2 |
| C2×C3×#817 | 2 |
| C3×#4995 | 2 |
| C3×#4554 | 2 |
| C3×#4552 | 2 |
| C3×#2090 | 3 |
| #70533 | 3 |