Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
528 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #20285466 | C2 | semidirect |
| 2. #20276627 | C2 | semidirect |
| 3. #20272723 | C2 | semidirect |
| 4. #20272639 | C2 | semidirect |
| 5. C53×#1999 | C2 | semidirect |
| 13. C22⋊#11719908 | C22 | semidirect |
| 14. C22×D8×C53 | C22 | semidirect |
| 18. C53×#340 | C22 | semidirect |
| 22. C2×D424 | D4 | semidirect |
| 32. #13133151 | D4 | semidirect |
| 103. C23×C53 | D16 | semidirect |
| 166. #1999 | D53 | semidirect |
| 177. C22×D8 | C2×D53 | semidirect |
| 189. #340 | C2×D53 | semidirect |
| 190. C53 | #12102 | semidirect |
| 279. C23 | #13133158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285466 | 2 |
| #20276627 | 2 |
| #20272723 | 2 |
| #20272639 | 2 |
| C53×#1999 | 2 |
| #12102 | 53 |