Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
552 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20274742 | C2 | semidirect |
| 4. #20274493 | C2 | semidirect |
| 5. #20273287 | C2 | semidirect |
| 7. C53×#1996 | C2 | semidirect |
| 8. C22×#11719924 | C4 | semidirect |
| 16. C2×#13133148 | C4 | semidirect |
| 17. C2×#13133141 | C4 | semidirect |
| 18. C2×#13133137 | C4 | semidirect |
| 194. #88322 | #99 | semidirect |
| 225. #1996 | D53 | semidirect |
| 262. C53 | #9786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810854 | 2 |
| #20275551 | 2 |
| #20274742 | 2 |
| #20274493 | 2 |
| #20273287 | 2 |
| #20273282 | 2 |
| C53×#1996 | 2 |
| #9786 | 53 |