Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
978 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 978 conjugacy classes of subgroups — too many to draw. Only its 221 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. #10592910 | C2 | semidirect |
| 3. #10592906 | C2 | semidirect |
| 4. #10589403 | C2 | semidirect |
| 7. C22×C32×D4 | C4 | semidirect |
| 11. C32×#121 | C4 | semidirect |
| 13. C2×C32×C4⋊C4 | C4 | semidirect |
| 18. #63658 | C22 | semidirect |
| 20. #63657 | C22 | semidirect |
| 51. C22×C3×D4 | Dic3 | semidirect |
| 55. C3×#121 | Dic3 | semidirect |
| 57. C2×C3×C4⋊C4 | Dic3 | semidirect |
| 145. C22×D4 | C3⋊Dic3 | semidirect |
| 150. #121 | C3⋊Dic3 | semidirect |
| 152. C2×C4⋊C4 | C3⋊Dic3 | semidirect |
| 241. C32 | #1510 | semidirect |
| 300. C3 | #71674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#121 | 2 |
| #10592910 | 2 |
| #10592906 | 2 |
| #10589403 | 2 |
| #71674 | 3 |