Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
426 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #20275000 | C2 | semidirect |
| 5. #20274937 | C2 | semidirect |
| 6. #20272845 | C2 | semidirect |
| 7. C53×#1392 | C2 | semidirect |
| 190. #1392 | D53 | semidirect |
| 218. C53 | #12962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283767 | 2 |
| #20276357 | 2 |
| #20275131 | 2 |
| #20275000 | 2 |
| #20274937 | 2 |
| #20272845 | 2 |
| C53×#1392 | 2 |
| #12962 | 53 |