Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
552 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20276290 | C2 | semidirect |
| 2. #20275887 | C2 | semidirect |
| 3. #20275691 | C2 | semidirect |
| 4. #20275386 | C2 | semidirect |
| 6. #20274865 | C2 | semidirect |
| 7. #20274820 | C2 | semidirect |
| 8. #104×Dic53 | C2 | semidirect |
| 188. C53 | #29232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276290 | 2 |
| #20275887 | 2 |
| #20275691 | 2 |
| #20275386 | 2 |
| #20275218 | 2 |
| #20274865 | 2 |
| #20274820 | 2 |
| #104×Dic53 | 2 |
| C53×#2050 | 2 |
| #29232 | 53 |