Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1686 conjugacy classes of subgroups; only the 503 normal subgroups are shown.
This group has 1686 conjugacy classes of subgroups — too many to draw. Only its 503 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. C2×C22⋊PSU(3,𝔽2) | C2 | semidirect |
| 4. D4×PSU(3,𝔽2) | C2 | direct (N × H) |
| 5. C2×C4⋊PSU(3,𝔽2) | C2 | semidirect |
| 6. C2×C4×PSU(3,𝔽2) | C2 | semidirect |
| 11. C22×PSU(3,𝔽2) | C22 | semidirect |
| 17. C22⋊PSU(3,𝔽2) | C22 | semidirect |
| 20. C4⋊PSU(3,𝔽2) | C22 | semidirect |
| 21. C4×PSU(3,𝔽2) | C22 | semidirect |
| 30. C2×PSU(3,𝔽2) | D4 | direct (N × H) |
| 33. C2×C32×D4 | Q8 | semidirect |
| 34. C2×#638 | Q8 | semidirect |
| 35. D4×C3⋊D3 | Q8 | semidirect |
| 37. C2×C4⋊(C3⋊D3) | Q8 | semidirect |
| 46. C23×C32 | C2×Q8 | semidirect |
| 49. C22×C3⋊D3 | C2×Q8 | semidirect |
| 50. C22×C3⋊D3 | C2×Q8 | semidirect |
| 61. PSU(3,𝔽2) | C2×D4 | direct (N × H) |
| 62. C32×D4 | C2×Q8 | semidirect |
| 63. C2×C32×C4 | C2×Q8 | semidirect |
| 64. #638 | C2×Q8 | semidirect |
| 65. C2×C3⋊Dic3 | C2×Q8 | semidirect |
| 66. C4⋊(C3⋊D3) | C2×Q8 | semidirect |
| 67. C4×C3⋊D3 | C2×Q8 | semidirect |
| 84. C22×C32 | C22×Q8 | semidirect |
| 91. C2×C3⋊D3 | C22×Q8 | semidirect |
| 97. C32×C4 | C22×Q8 | semidirect |
| 98. C3⋊Dic3 | C22×Q8 | semidirect |
| 129. C2×C32 | D4×Q8 | semidirect |
| 132. C3⋊D3 | D4×Q8 | semidirect |
| 145. C2×D4 | PSU(3,𝔽2) | direct (N × H) |
| 171. C32 | C2×D4×Q8 | semidirect |
| 178. C23 | C2×PSU(3,𝔽2) | semidirect |
| 183. D4 | C2×PSU(3,𝔽2) | direct (N × H) |
| 194. C2×C4 | C2×PSU(3,𝔽2) | semidirect |
| 213. C22 | C22×PSU(3,𝔽2) | semidirect |
| 218. C4 | C22×PSU(3,𝔽2) | semidirect |
| 225. C2 | D4×PSU(3,𝔽2) | 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 |
| C2×D4×#157 | 2 |
| C2×C22⋊PSU(3,𝔽2) | 2 |
| D4×PSU(3,𝔽2) | 2 |
| C2×C4⋊PSU(3,𝔽2) | 2 |
| C2×C4×PSU(3,𝔽2) | 2 |
| C2×D4×Q8 | 9 |