Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
350 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 1. #10592596 | C2 | semidirect |
| 2. #10590929 | C2 | semidirect |
| 3. C2×#63546 | C2 | semidirect |
| 4. #10590624 | C2 | semidirect |
| 5. C3×#4495 | C2 | semidirect |
| 6. C3×#4493 | C2 | semidirect |
| 7. #10589128 | C2 | semidirect |
| 38. #4495 | D3 | semidirect |
| 39. #4493 | D3 | semidirect |
| 288. C32 | #2221 | semidirect |
| 329. C3 | #69260 | semidirect |
| 330. C3 | #69361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592596 | 2 |
| #10590929 | 2 |
| C2×#63546 | 2 |
| #10590624 | 2 |
| C3×#4495 | 2 |
| C3×#4493 | 2 |
| #10589128 | 2 |
| #69361 | 3 |
| #69260 | 3 |