Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
528 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20276626 | C2 | semidirect |
| 2. #20275713 | C2 | semidirect |
| 3. #20272724 | C2 | semidirect |
| 4. #20272639 | C2 | semidirect |
| 5. C53×#3186 | C2 | semidirect |
| 6. C22×D424 | C22 | semidirect |
| 11. C22⋊#11719908 | C22 | semidirect |
| 12. #16810386 | C22 | semidirect |
| 34. C2×D8×C53 | D4 | semidirect |
| 44. #107×C53 | D4 | semidirect |
| 100. C23×C53 | D16 | semidirect |
| 164. #3186 | D53 | semidirect |
| 190. C53 | #12102 | semidirect |
| 199. C2×D8 | C22⋊D53 | semidirect |
| 215. #107 | C22⋊D53 | semidirect |
| 279. C23 | #13133158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276626 | 2 |
| #20275713 | 2 |
| #20272724 | 2 |
| #20272639 | 2 |
| C53×#3186 | 2 |
| #12102 | 53 |