Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
574 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
| 7. #10593555 | C2 | semidirect |
| 8. #10593555 | C2 | semidirect |
| 9. #10593555 | C2 | semidirect |
| 10. #10593551 | C2 | semidirect |
| 11. C4×#3777 | C2 | semidirect |
| 68. C32×C22⋊C4 | Q8 | semidirect |
| 69. #3757 | Q8 | semidirect |
| 70. #3752 | Q8 | semidirect |
| 71. #3752 | Q8 | semidirect |
| 247. C22⋊C4 | PSU(3,𝔽2) | semidirect |
| 272. C32 | #2492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊PSU(3,𝔽2) | 2 |
| C2×C4⋊PSU(3,𝔽2) | 2 |
| #10593747 | 2 |
| C22⋊C4×#157 | 2 |
| #10593570 | 2 |
| #10593568 | 2 |
| #10593555 | 2 |
| #10593551 | 2 |
| C4×#3777 | 2 |
| #2492 | 9 |