Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1008 conjugacy classes of subgroups; only the 321 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 321 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 |
|---|---|---|
| 69. C32×Q8 | Q16 | semidirect |
| 134. C3×Q8 | #216 | semidirect |
| 177. C32 | #3363 | semidirect |
| 182. Q8 | #3756 | semidirect |
| 205. C3 | #83707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q82 | 2 |
| #10596041 | 2 |
| #10592792 | 2 |
| #10592790 | 2 |
| #10592730 | 2 |
| C4×#3756 | 2 |
| Q8×C3⋊(C3⋊C8) | 2 |
| #83707 | 3 |