Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20275695 | C2 | semidirect |
| 4. #20273187 | C2 | semidirect |
| 5. #20272607 | C2 | semidirect |
| 6. #20272604 | C2 | semidirect |
| 9. #16811033 | C4 | semidirect |
| 10. #16811018 | C4 | semidirect |
| 11. #16810993 | C4 | semidirect |
| 12. #16810982 | C4 | semidirect |
| 233. C53 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285322 | 2 |
| #20275695 | 2 |
| #20273201 | 2 |
| #20273187 | 2 |
| #20272607 | 2 |
| #20272604 | 2 |
| C53×#2995 | 2 |
| #8998 | 53 |