Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
304 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 1. #20276531 | C2 | semidirect |
| 2. #20274470 | C2 | semidirect |
| 3. #20272709 | C2 | semidirect |
| 5. #20272703 | C2 | semidirect |
| 17. C53×#498 | C4 | semidirect |
| 18. C53×#495 | C4 | semidirect |
| 23. C53×#442 | C4 | semidirect |
| 24. C53×#441 | C4 | semidirect |
| 153. #498 | Dic53 | semidirect |
| 154. #495 | Dic53 | semidirect |
| 159. #442 | Dic53 | semidirect |
| 160. #441 | Dic53 | semidirect |
| 171. C53 | #11769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276531 | 2 |
| #20274470 | 2 |
| #20272709 | 2 |
| #20272706 | 2 |
| #20272703 | 2 |
| #20272700 | 2 |
| C53×#3173 | 2 |
| #11769 | 53 |