Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1410 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1410 conjugacy classes of subgroups — too many to draw. Only its 183 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. C23×PSU(3,𝔽2) | C2 | semidirect |
| 3. #10593570 | C2 | direct (N × H) |
| 4. C2×#63747 | C2 | semidirect |
| 9. C22×PSU(3,𝔽2) | C22 | semidirect |
| 12. #63747 | C22 | semidirect |
| 13. C24×C32 | Q8 | semidirect |
| 16. C23×C3⋊D3 | Q8 | semidirect |
| 17. C23×C3⋊D3 | Q8 | semidirect |
| 33. C23×C32 | C2×Q8 | semidirect |
| 42. C22×C3⋊D3 | C2×Q8 | semidirect |
| 102. C2×C32 | #393 | semidirect |
| 105. C3⋊D3 | #393 | semidirect |
| 114. C24 | PSU(3,𝔽2) | semidirect |
| 138. C32 | C2×#393 | semidirect |
| 152. C23 | C2×PSU(3,𝔽2) | semidirect |
| 189. C2 | #10593570 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×PSU(3,𝔽2) | 2 |
| C22×C22⋊#157 | 2 |
| #10593570 | 2 |
| C2×#63747 | 2 |
| C2×#393 | 9 |