Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20273353 | C2 | semidirect |
| 3. #20273266 | C2 | semidirect |
| 5. #20272587 | C2 | semidirect |
| 6. #20272580 | C2 | semidirect |
| 20. C53×#500 | C4 | semidirect |
| 21. C53×#492 | C4 | semidirect |
| 22. C53×#487 | C4 | semidirect |
| 23. C53×#486 | C4 | semidirect |
| 169. #500 | Dic53 | semidirect |
| 170. #492 | Dic53 | semidirect |
| 171. #487 | Dic53 | semidirect |
| 172. #486 | Dic53 | semidirect |
| 186. C53 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283786 | 2 |
| #20273353 | 2 |
| #20273266 | 2 |
| #20273262 | 2 |
| #20272587 | 2 |
| #20272580 | 2 |
| C53×#3182 | 2 |
| #9415 | 53 |