Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
748 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20275547 | C2 | semidirect |
| 3. #20273445 | C2 | semidirect |
| 4. #20273438 | C2 | semidirect |
| 5. #20273349 | C2 | semidirect |
| 6. #20273222 | C2 | semidirect |
| 7. C53×#1506 | C2 | semidirect |
| 10. #16811333 | C4 | semidirect |
| 12. #16811295 | C4 | semidirect |
| 221. #1506 | D53 | semidirect |
| 254. C53 | #8493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289115 | 2 |
| #20275547 | 2 |
| #20273445 | 2 |
| #20273438 | 2 |
| #20273349 | 2 |
| #20273222 | 2 |
| C53×#1506 | 2 |
| #8493 | 53 |