Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1176 conjugacy classes of subgroups; only the 321 normal subgroups are shown.
This group has 1176 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 |
|---|---|---|
| 1. C32×Q82 | C2 | semidirect |
| 3. #10592787 | C2 | semidirect |
| 4. #10592783 | C2 | semidirect |
| 5. #10592726 | C2 | semidirect |
| 6. C4×#3755 | C2 | semidirect |
| 7. Q8×C3⋊(C3⋊C8) | C2 | semidirect |
| 25. C3×Q82 | D3 | semidirect |
| 71. C32×Q8 | SD16 | semidirect |
| 72. C32×Q8 | #41 | semidirect |
| 86. Q82 | C3⋊D3 | semidirect |
| 142. C3×Q8 | #215 | semidirect |
| 143. C3×Q8 | #239 | semidirect |
| 191. C32 | #3362 | semidirect |
| 195. Q8 | #3755 | semidirect |
| 196. Q8 | #3832 | semidirect |
| 225. C3 | #83703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q82 | 2 |
| #10596048 | 2 |
| #10592787 | 2 |
| #10592783 | 2 |
| #10592726 | 2 |
| C4×#3755 | 2 |
| Q8×C3⋊(C3⋊C8) | 2 |
| #83703 | 3 |