Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
434 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 101 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. C4⋊C16×D53 | C2 | semidirect |
| 3. #334×D53 | C2 | semidirect |
| 4. #20272759 | C2 | semidirect |
| 5. #20272758 | C2 | semidirect |
| 6. #20272757 | C2 | semidirect |
| 7. C53×#1360 | C2 | semidirect |
| 20. C4⋊#11719908 | C22 | semidirect |
| 22. #16810374 | C22 | semidirect |
| 25. C53×C4⋊C16 | C22 | semidirect |
| 26. C53×#334 | C22 | semidirect |
| 179. #1360 | D53 | direct (N × H) |
| 185. D53 | #1360 | direct (N × H) |
| 201. C4⋊C16 | C2×D53 | semidirect |
| 204. #334 | C2×D53 | semidirect |
| 205. C53 | C2×#1360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #495×D53 | 2 |
| C4⋊C16×D53 | 2 |
| #334×D53 | 2 |
| #20272759 | 2 |
| #20272758 | 2 |
| #20272757 | 2 |
| C53×#1360 | 2 |
| C2×#1360 | 53 |