Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 147 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. C2×#64225 | C2 | semidirect |
| 2. #10594008 | C2 | semidirect |
| 3. C4×#3787 | C2 | semidirect |
| 4. #10593418 | C2 | semidirect |
| 8. C2×#3774 | C22 | semidirect |
| 13. #63914 | C22 | semidirect |
| 14. C4×#622 | C22 | semidirect |
| 26. #3787 | D4 | semidirect |
| 47. C4×C3⋊D3 | D8 | semidirect |
| 53. #622 | C2×D4 | semidirect |
| 79. C32×C4 | C2×D8 | semidirect |
| 80. C3⋊Dic3 | C2×D8 | semidirect |
| 111. C3⋊D3 | #493 | semidirect |
| 140. C32 | C2×#493 | semidirect |
| 169. C4 | #64225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64225 | 2 |
| #10594008 | 2 |
| C4×#3787 | 2 |
| #10593418 | 2 |
| C2×#493 | 9 |