Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
490 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #20273227 | C2 | semidirect |
| 5. #20272608 | C2 | semidirect |
| 6. #20272607 | C2 | semidirect |
| 7. C53×#1506 | C2 | semidirect |
| 9. #16810985 | C4 | semidirect |
| 10. #16810985 | C4 | semidirect |
| 54. #13133128 | C2×C4 | semidirect |
| 61. C4⋊Q8×C53 | C2×C4 | semidirect |
| 62. C4⋊Q8×C53 | C2×C4 | semidirect |
| 202. #1506 | D53 | semidirect |
| 234. C53 | #9439 | semidirect |
| 239. C4⋊Q8 | C4×D53 | semidirect |
| 240. C4⋊Q8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285104 | 2 |
| #20277825 | 2 |
| #20273338 | 2 |
| #20273227 | 2 |
| #20272608 | 2 |
| #20272607 | 2 |
| C53×#1506 | 2 |
| #9439 | 53 |