Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1042 conjugacy classes of subgroups; only the 447 normal subgroups are shown.
This group has 1042 conjugacy classes of subgroups — too many to draw. Only its 447 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 |
|---|---|---|
| 3. #10596547 | C2 | semidirect |
| 4. #10596547 | C2 | semidirect |
| 5. Q8×PSU(3,𝔽2) | C2 | semidirect |
| 29. C2×C32×Q8 | Q8 | semidirect |
| 30. Q8×C3⋊D3 | Q8 | semidirect |
| 33. C2×#634 | Q8 | semidirect |
| 121. C2×Q8 | PSU(3,𝔽2) | semidirect |
| 143. C32 | #3502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596646 | 2 |
| C2×Q8×#157 | 2 |
| #10596547 | 2 |
| Q8×PSU(3,𝔽2) | 2 |
| #10596543 | 2 |
| #10596542 | 2 |
| #3502 | 9 |