Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20274920 | C2 | semidirect |
| 5. #20272603 | C2 | semidirect |
| 6. #20272602 | C2 | semidirect |
| 7. C53×#1855 | C2 | semidirect |
| 138. C22×D53 | #108 | semidirect |
| 202. #1855 | D53 | semidirect |
| 235. C53 | #8859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283742 | 2 |
| #20275012 | 2 |
| #20274920 | 2 |
| #20273031 | 2 |
| #20272603 | 2 |
| #20272602 | 2 |
| C53×#1855 | 2 |
| #8859 | 53 |