Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
351 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 351 conjugacy classes of subgroups — too many to draw. Only its 114 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. #70964 | C3 | direct (N × H) |
| 82. C32×C8 | Q16 | semidirect |
| 174. C3×C8 | #216 | semidirect |
| 175. C3×C8 | C3×Q16 | semidirect |
| 216. C32 | #1694 | semidirect |
| 229. C8 | C3×#216 | semidirect |
| 248. C3 | #70964 | direct (N × H) |
| 249. C3 | C3×#1694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#446 | 2 |
| C3×#5031 | 2 |
| C3×#4682 | 2 |
| C3×#4486 | 2 |
| C3×#4457 | 2 |
| C3×#1694 | 3 |
| #70964 | 3 |