Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
738 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 234 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 |
|---|---|---|
| 6. #10593750 | C2 | direct (N × H) |
| 27. C2×#634 | C8 | semidirect |
| 31. C2×#622 | Q8 | semidirect |
| 62. #634 | C2×C8 | semidirect |
| 65. #622 | C2×Q8 | semidirect |
| 124. C2×C32 | C8×Q8 | semidirect |
| 158. C32 | C2×C8×Q8 | semidirect |
| 192. C2 | #10593750 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64096 | 2 |
| C2×#63779 | 2 |
| C2×C4⋊#622 | 2 |
| C2×C4×#622 | 2 |
| #10593750 | 2 |
| C2×C8×Q8 | 9 |