Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
688 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 215 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. #20275211 | C2 | semidirect |
| 2. #20275190 | C2 | semidirect |
| 3. #20275109 | C2 | semidirect |
| 5. #20274864 | C2 | semidirect |
| 20. C53×#497 | C4 | semidirect |
| 21. C53×#494 | C4 | semidirect |
| 22. C53×#492 | C4 | semidirect |
| 139. #497 | Dic53 | semidirect |
| 140. #494 | Dic53 | semidirect |
| 141. #492 | Dic53 | semidirect |
| 151. C53 | #23360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275211 | 2 |
| #20275190 | 2 |
| #20275109 | 2 |
| #20275099 | 2 |
| #20274864 | 2 |
| C53×#3152 | 2 |
| #23360 | 53 |