Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
422 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 422 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 |
|---|---|---|
| 8. #10593537 | C2 | direct (N × H) |
| 38. C2×#622 | Q8 | semidirect |
| 49. #3787 | Q8 | semidirect |
| 54. C2×C32×C8 | Q8 | semidirect |
| 55. C2×C3⋊(C3⋊C8) | Q8 | semidirect |
| 56. C8×C3⋊D3 | Q8 | semidirect |
| 80. #622 | C2×Q8 | semidirect |
| 81. C32×C8 | C2×Q8 | semidirect |
| 82. C3⋊(C3⋊C8) | C2×Q8 | semidirect |
| 140. C2×C32 | #501 | semidirect |
| 142. C3⋊D3 | #501 | semidirect |
| 160. C2×C8 | PSU(3,𝔽2) | semidirect |
| 183. C32 | C2×#501 | semidirect |
| 206. C8 | C2×PSU(3,𝔽2) | semidirect |
| 231. C2 | #10593537 | direct (N × H) |
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 |
| C2×#64243 | 2 |
| C2×#63769 | 2 |
| C2×#63768 | 2 |
| C2×#63767 | 2 |
| C2×#63746 | 2 |
| C2×#63745 | 2 |
| #10593537 | 2 |
| C2×#501 | 9 |