Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
522 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. C2×#63654 | C2 | semidirect |
| 3. C2×#63627 | C2 | semidirect |
| 4. #10592572 | C2 | semidirect |
| 5. C32×#357 | C2 | semidirect |
| 6. #10589367 | C2 | semidirect |
| 7. #10589357 | C2 | semidirect |
| 26. C3×#357 | D3 | semidirect |
| 44. #3746 | D4 | semidirect |
| 87. #357 | C3⋊D3 | semidirect |
| 120. C3⋊Dic3 | SD32 | semidirect |
| 190. C32 | #2207 | semidirect |
| 227. C3 | #69204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592850 | 2 |
| C2×#63654 | 2 |
| C2×#63627 | 2 |
| #10592572 | 2 |
| C32×#357 | 2 |
| #10589367 | 2 |
| #10589357 | 2 |
| #69204 | 3 |