Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
386 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 4. #10590169 | C2 | semidirect |
| 5. C8×#622 | C2 | semidirect |
| 23. #3792 | C8 | direct (N × H) |
| 56. #622 | C2×C8 | semidirect |
| 58. C32×C8 | M16 | semidirect |
| 60. C3⋊(C3⋊C8) | M16 | semidirect |
| 149. C32 | C8×M16 | semidirect |
| 166. C8 | #3792 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593801 | 2 |
| C4×#3792 | 2 |
| C2×C8×C3⋊Dic3 | 2 |
| #10590169 | 2 |
| C8×#622 | 2 |
| C8×M16 | 9 |