Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
598 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×C4⋊PSU(3,𝔽2) | C2 | semidirect |
| 4. #10593558 | C2 | direct (N × H) |
| 5. C2×#63746 | C2 | semidirect |
| 6. C2×#63744 | C2 | semidirect |
| 19. C4⋊PSU(3,𝔽2) | C22 | semidirect |
| 21. #63746 | C22 | semidirect |
| 22. #63744 | C22 | semidirect |
| 32. C2×C32×D4 | Q8 | semidirect |
| 36. D4×C3⋊D3 | Q8 | semidirect |
| 38. C2×C4⋊(C3⋊D3) | Q8 | semidirect |
| 71. C32×D4 | C2×Q8 | semidirect |
| 77. C4⋊(C3⋊D3) | C2×Q8 | semidirect |
| 154. C2×C32 | #474 | semidirect |
| 157. C3⋊D3 | #474 | semidirect |
| 169. C2×D4 | PSU(3,𝔽2) | semidirect |
| 204. C32 | C2×#474 | semidirect |
| 218. D4 | C2×PSU(3,𝔽2) | semidirect |
| 268. C2 | #10593558 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#157 | 2 |
| C2×C4⋊PSU(3,𝔽2) | 2 |
| C2×#63782 | 2 |
| #10593558 | 2 |
| C2×#63746 | 2 |
| C2×#63744 | 2 |
| C2×#474 | 9 |