Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20276469 | C2 | semidirect |
| 3. #20273460 | C2 | semidirect |
| 4. #20272759 | C2 | semidirect |
| 5. #20272758 | C2 | semidirect |
| 6. #20272757 | C2 | semidirect |
| 7. C53×#1360 | C2 | semidirect |
| 20. C4⋊#11719908 | C22 | semidirect |
| 23. #16810374 | C22 | semidirect |
| 25. C53×C4⋊C16 | C22 | semidirect |
| 26. C53×#334 | C22 | semidirect |
| 178. #1360 | D53 | semidirect |
| 200. C4⋊C16 | C2×D53 | semidirect |
| 203. #334 | C2×D53 | semidirect |
| 204. C53 | #11926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #495×D53 | 2 |
| #20276469 | 2 |
| #20273460 | 2 |
| #20272759 | 2 |
| #20272758 | 2 |
| #20272757 | 2 |
| C53×#1360 | 2 |
| #11926 | 53 |