Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
794 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 143 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×C22⋊PSU(3,𝔽2) | C2 | semidirect |
| 3. C2×C4⋊PSU(3,𝔽2) | C2 | semidirect |
| 5. #10593566 | C2 | semidirect |
| 6. #10593553 | C2 | semidirect |
| 7. C4×#3777 | C2 | semidirect |
| 34. C2×C32×D4 | Q8 | semidirect |
| 35. C2×#638 | Q8 | semidirect |
| 38. C2×C4⋊(C3⋊D3) | Q8 | semidirect |
| 48. #3777 | D4 | semidirect |
| 109. C32×C4 | C22⋊Q8 | semidirect |
| 110. C3⋊Dic3 | C22⋊Q8 | semidirect |
| 155. C2×D4 | PSU(3,𝔽2) | semidirect |
| 187. C32 | #2542 | semidirect |
| 240. C4 | C22⋊PSU(3,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#157 | 2 |
| C2×C22⋊PSU(3,𝔽2) | 2 |
| C2×C4⋊PSU(3,𝔽2) | 2 |
| #10593827 | 2 |
| #10593566 | 2 |
| #10593553 | 2 |
| C4×#3777 | 2 |
| #2542 | 9 |