Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20275559 | C2 | semidirect |
| 4. #20273399 | C2 | semidirect |
| 6. #20272628 | C2 | semidirect |
| 7. C53×#1299 | C2 | semidirect |
| 151. Dic106 | #101 | semidirect |
| 185. #1299 | D53 | semidirect |
| 214. C53 | #9358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284531 | 2 |
| #20283844 | 2 |
| #20275559 | 2 |
| #20273399 | 2 |
| #20273155 | 2 |
| #20272628 | 2 |
| C53×#1299 | 2 |
| #9358 | 53 |