Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
530 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #20275536 | C2 | semidirect |
| 5. #20272597 | C2 | semidirect |
| 6. #20272596 | C2 | semidirect |
| 7. C53×#1993 | C2 | semidirect |
| 10. #16810985 | C4 | semidirect |
| 55. #13133128 | C2×C4 | semidirect |
| 65. C4⋊Q8×C53 | C2×C4 | semidirect |
| 211. #1993 | D53 | semidirect |
| 246. C53 | #8999 | semidirect |
| 257. C4⋊Q8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810985 | 2 |
| #20277886 | 2 |
| #20275536 | 2 |
| C2×#16810362 | 2 |
| #20272597 | 2 |
| #20272596 | 2 |
| C53×#1993 | 2 |
| #8999 | 53 |