Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1670 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 1670 conjugacy classes of subgroups — too many to draw. Only its 455 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 |
|---|---|---|
| 2. #10596550 | C2 | direct (N × H) |
| 3. C2×C22⋊PSU(3,𝔽2) | C2 | semidirect |
| 6. C22×PSU(3,𝔽2) | C22 | semidirect |
| 9. C22⋊PSU(3,𝔽2) | C22 | semidirect |
| 10. C2×#3777 | C22 | semidirect |
| 11. C24×C32 | Q8 | semidirect |
| 13. C23×C3⋊D3 | Q8 | semidirect |
| 14. C23×C3⋊D3 | Q8 | semidirect |
| 21. C2×PSU(3,𝔽2) | C23 | semidirect |
| 23. #3777 | C23 | semidirect |
| 28. C23×C32 | C2×Q8 | semidirect |
| 35. C22×C3⋊D3 | C2×Q8 | semidirect |
| 84. C2×C32 | #543 | semidirect |
| 87. C3⋊D3 | #543 | semidirect |
| 94. C24 | PSU(3,𝔽2) | semidirect |
| 114. C32 | C2×#543 | semidirect |
| 126. C23 | C2×PSU(3,𝔽2) | semidirect |
| 155. C2 | #10596550 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#157 | 2 |
| #10596550 | 2 |
| C2×C22⋊PSU(3,𝔽2) | 2 |
| C2×#543 | 9 |