Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
510 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 102 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. C2×C4⋊PSU(3,𝔽2) | C2 | semidirect |
| 3. #10596484 | C2 | semidirect |
| 4. #10596418 | C2 | semidirect |
| 5. #10596409 | C2 | semidirect |
| 6. #10596408 | C2 | semidirect |
| 7. #10596404 | C2 | semidirect |
| 77. C2×C32×C4 | SD16 | semidirect |
| 78. C2×C3⋊Dic3 | SD16 | semidirect |
| 79. C4×C3⋊D3 | SD16 | semidirect |
| 80. C4×C3⋊D3 | SD16 | semidirect |
| 224. C32 | #3206 | semidirect |
| 253. C2×C4 | AΓL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊PSU(3,𝔽2) | 2 |
| #10596511 | 2 |
| #10596484 | 2 |
| #10596418 | 2 |
| #10596409 | 2 |
| #10596408 | 2 |
| #10596404 | 2 |
| #3206 | 9 |