Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
686 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 182 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. #10593835 | C2 | semidirect |
| 3. Q8×#622 | C2 | semidirect |
| 27. #3792 | Q8 | direct (N × H) |
| 47. C32×Q8 | M16 | semidirect |
| 59. #622 | C2×Q8 | semidirect |
| 147. C32 | Q8×M16 | semidirect |
| 150. Q8 | #3792 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C3⋊Dic3 | 2 |
| #10593835 | 2 |
| Q8×#622 | 2 |
| #10593805 | 2 |
| C4×#3792 | 2 |
| Q8×M16 | 9 |