Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
344 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20276665 | C2 | semidirect |
| 3. #20276021 | C2 | semidirect |
| 4. #20272703 | C2 | semidirect |
| 5. #20272700 | C2 | semidirect |
| 6. #20272668 | C2 | semidirect |
| 7. C53×#3263 | C2 | semidirect |
| 167. #3263 | D53 | semidirect |
| 198. C53 | #12172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276665 | 2 |
| #20276660 | 2 |
| #20276021 | 2 |
| #20272703 | 2 |
| #20272700 | 2 |
| #20272668 | 2 |
| C53×#3263 | 2 |
| #12172 | 53 |