Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20283092 | C2 | semidirect |
| 5. #20273401 | C2 | semidirect |
| 6. #20272547 | C2 | semidirect |
| 7. C53×#1546 | C2 | semidirect |
| 174. #1546 | D53 | semidirect |
| 202. C53 | #10286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285845 | 2 |
| #20285836 | 2 |
| #20283092 | 2 |
| #20275542 | 2 |
| #20273401 | 2 |
| #20272547 | 2 |
| C53×#1546 | 2 |
| #10286 | 53 |