Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
594 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 594 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 |
|---|---|---|
| 2. #20275552 | C2 | semidirect |
| 3. #20275550 | C2 | semidirect |
| 4. #20274738 | C2 | semidirect |
| 5. #20274494 | C2 | semidirect |
| 6. #20273284 | C2 | semidirect |
| 7. C53×#1519 | C2 | semidirect |
| 8. C22×#11719922 | C4 | semidirect |
| 15. C2×#13133150 | C4 | semidirect |
| 17. C2×#13133138 | C4 | semidirect |
| 18. C2×#13133137 | C4 | semidirect |
| 202. #88322 | #99 | semidirect |
| 241. #1519 | D53 | semidirect |
| 274. C53 | #9785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810857 | 2 |
| #20275552 | 2 |
| #20275550 | 2 |
| #20274738 | 2 |
| #20274494 | 2 |
| #20273284 | 2 |
| C53×#1519 | 2 |
| #9785 | 53 |