Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20276513 | C2 | semidirect |
| 3. #20273475 | C2 | semidirect |
| 4. #20272759 | C2 | semidirect |
| 5. #20272758 | C2 | semidirect |
| 6. #20272757 | C2 | semidirect |
| 7. C53×#1360 | C2 | semidirect |
| 19. C4⋊#11719908 | C22 | semidirect |
| 23. #16810374 | C22 | semidirect |
| 25. C53×C4⋊C16 | C22 | semidirect |
| 26. C53×#334 | C22 | semidirect |
| 177. #1360 | D53 | semidirect |
| 197. C4⋊C16 | C2×D53 | semidirect |
| 202. #334 | C2×D53 | semidirect |
| 203. C53 | #11957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #495×D53 | 2 |
| #20276513 | 2 |
| #20273475 | 2 |
| #20272759 | 2 |
| #20272758 | 2 |
| #20272757 | 2 |
| C53×#1360 | 2 |
| #11957 | 53 |