Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
401 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 401 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 9. #71341 | C3 | direct (N × H) |
| 97. C32×C8 | Q16 | semidirect |
| 202. C3×C8 | #216 | semidirect |
| 203. C3×C8 | C3×Q16 | semidirect |
| 248. C32 | #1723 | semidirect |
| 262. C8 | C3×#216 | semidirect |
| 281. C3 | #71341 | direct (N × H) |
| 282. C3 | C3×#1723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#498 | 2 |
| C3×#5093 | 2 |
| C3×#5092 | 2 |
| C3×#5079 | 2 |
| C3×#5078 | 2 |
| C3×#4682 | 2 |
| C3×#4455 | 2 |
| C3×#1723 | 3 |
| #71341 | 3 |