Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 102 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. #20290932 | C2 | semidirect |
| 4. #20290535 | C2 | semidirect |
| 5. #20289794 | C2 | semidirect |
| 6. #20289784 | C2 | semidirect |
| 13. #16811542 | C4 | semidirect |
| 14. #16811541 | C4 | semidirect |
| 15. #16811538 | C4 | semidirect |
| 16. #16811537 | C4 | semidirect |
| 221. C53 | #12651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291043 | 2 |
| #20291029 | 2 |
| #20290932 | 2 |
| #20290535 | 2 |
| #20289794 | 2 |
| #20289784 | 2 |
| #444×D53 | 2 |
| #12651 | 53 |