Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
766 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 135 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×C22⋊PSU(3,𝔽2) | C2 | semidirect |
| 4. C22×#3777 | C2 | semidirect |
| 6. #10593568 | C2 | semidirect |
| 7. #10593568 | C2 | semidirect |
| 8. #10593567 | C2 | semidirect |
| 9. #10593555 | C2 | semidirect |
| 10. #10593552 | C2 | semidirect |
| 11. #10593548 | C2 | semidirect |
| 61. C2×C32×D4 | Q8 | semidirect |
| 62. C2×#638 | Q8 | semidirect |
| 63. C2×#638 | Q8 | semidirect |
| 66. C2×C4⋊(C3⋊D3) | Q8 | semidirect |
| 81. #3777 | D4 | semidirect |
| 162. C22×C32 | C22⋊Q8 | semidirect |
| 177. C2×C3⋊D3 | C22⋊Q8 | semidirect |
| 267. C2×D4 | PSU(3,𝔽2) | semidirect |
| 329. C32 | #2417 | semidirect |
| 419. C22 | 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 |
| C22×#3777 | 2 |
| #10593826 | 2 |
| #10593568 | 2 |
| #10593567 | 2 |
| #10593555 | 2 |
| #10593552 | 2 |
| #10593548 | 2 |
| #2417 | 9 |