Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
415 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 415 conjugacy classes of subgroups — too many to draw. Only its 94 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. #10590290 | C2 | semidirect |
| 5. #10590288 | C2 | semidirect |
| 6. #10590287 | C2 | semidirect |
| 7. C3⋊C82 | C2 | semidirect |
| 261. C32 | #1711 | semidirect |
| 301. C3 | #71183 | semidirect |
| 302. C3 | #71183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592769 | 2 |
| C3×#5070 | 2 |
| #10590290 | 2 |
| #10590288 | 2 |
| #10590287 | 2 |
| C3⋊C82 | 2 |
| #71183 | 3 |