Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
684 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 1. Q8×#634 | C2 | semidirect |
| 5. #10589401 | C2 | semidirect |
| 6. #10589350 | C2 | semidirect |
| 7. #10589347 | C2 | semidirect |
| 78. C32×Q8 | SD16 | semidirect |
| 95. #634 | SD16 | semidirect |
| 164. C3×Q8 | #214 | semidirect |
| 228. C32 | #1623 | semidirect |
| 235. Q8 | #3754 | semidirect |
| 270. C3 | #71033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#634 | 2 |
| C32×#460 | 2 |
| #10592775 | 2 |
| #10592774 | 2 |
| #10589401 | 2 |
| #10589350 | 2 |
| #10589347 | 2 |
| #71033 | 3 |