Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
516 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 161 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. C32×C8×Q8 | C2 | semidirect |
| 3. #10592719 | C2 | semidirect |
| 6. #10589348 | C2 | semidirect |
| 7. #10589323 | C2 | semidirect |
| 24. C3×C8×Q8 | D3 | semidirect |
| 68. C32×Q8 | SD16 | semidirect |
| 84. C32×C8 | SD16 | semidirect |
| 90. C8×Q8 | C3⋊D3 | semidirect |
| 142. C3×Q8 | #204 | semidirect |
| 158. C3×C8 | #215 | semidirect |
| 196. C32 | #1666 | semidirect |
| 201. Q8 | #3744 | semidirect |
| 217. C8 | #3755 | semidirect |
| 234. C3 | #70938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C8×Q8 | 2 |
| #10592726 | 2 |
| #10592719 | 2 |
| #10592392 | 2 |
| #10589351 | 2 |
| #10589348 | 2 |
| #10589323 | 2 |
| #70938 | 3 |