Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
644 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #20274651 | C2 | semidirect |
| 4. #20274638 | C2 | semidirect |
| 6. #20272622 | C2 | semidirect |
| 7. C53×#1293 | C2 | semidirect |
| 12. #16810781 | C4 | semidirect |
| 14. #16810764 | C4 | semidirect |
| 249. #1293 | D53 | semidirect |
| 283. C53 | #9519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283952 | 2 |
| #20283760 | 2 |
| #20274651 | 2 |
| #20274638 | 2 |
| #20273259 | 2 |
| #20272622 | 2 |
| C53×#1293 | 2 |
| #9519 | 53 |