Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
490 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 12. #63779 | C4 | semidirect |
| 14. C4×#622 | C4 | semidirect |
| 32. #3750 | C8 | semidirect |
| 62. #622 | C4⋊C4 | semidirect |
| 86. C3⋊Dic3 | C4×C8 | semidirect |
| 156. C32 | C8×C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63779 | 2 |
| C2×C4×#622 | 2 |
| #10592348 | 2 |
| #10590207 | 2 |
| C8×C4⋊C4 | 9 |