Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
467 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 467 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 4. #10590312 | C2 | semidirect |
| 5. #10590303 | C2 | semidirect |
| 6. #10590287 | C2 | semidirect |
| 7. #10589079 | C2 | semidirect |
| 100. C3⋊(C3⋊C8) | SD16 | semidirect |
| 270. C32 | #1714 | semidirect |
| 310. C3 | #71184 | semidirect |
| 311. C3 | #71257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592775 | 2 |
| C3×#5076 | 2 |
| C3×#5070 | 2 |
| #10590312 | 2 |
| #10590303 | 2 |
| #10590287 | 2 |
| #10589079 | 2 |
| #71257 | 3 |
| #71184 | 3 |