Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 92 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. #20290473 | C2 | semidirect |
| 4. #20289814 | C2 | semidirect |
| 6. C2×#13133304 | C4 | semidirect |
| 10. #16811627 | C4 | semidirect |
| 12. #16811597 | C4 | semidirect |
| 15. C4×D53⋊C8 | C4 | semidirect |
| 16. #16811534 | C4 | semidirect |
| 17. #16811531 | C4 | semidirect |
| 180. C53 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291437 | 2 |
| #20291007 | 2 |
| #20290473 | 2 |
| #20289814 | 2 |
| #20276377 | 2 |
| #12633 | 53 |