Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20283092 | C2 | semidirect |
| 4. #20273400 | C2 | semidirect |
| 5. #20273399 | C2 | semidirect |
| 6. #20272547 | C2 | semidirect |
| 200. C53 | #10285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285840 | 2 |
| #20283092 | 2 |
| #20275544 | 2 |
| #20273400 | 2 |
| #20273399 | 2 |
| #20272547 | 2 |
| C53×#3227 | 2 |
| #10285 | 53 |