Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
391 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 391 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. #10590385 | C2 | semidirect |
| 4. #10590250 | C2 | semidirect |
| 6. #10589100 | C2 | semidirect |
| 7. #10589094 | C2 | semidirect |
| 306. C32 | #1682 | semidirect |
| 353. C3 | #68411 | semidirect |
| 354. C3 | #71023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592769 | 2 |
| C3×#5075 | 2 |
| #10590385 | 2 |
| #10590250 | 2 |
| C3×#4544 | 2 |
| #10589100 | 2 |
| #10589094 | 2 |
| #71023 | 3 |
| #68411 | 3 |