Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
248 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#13133157 | C4 | semidirect |
| 5. C22×#11719908 | C4 | semidirect |
| 15. C53×#349 | C4 | semidirect |
| 125. #349 | Dic53 | semidirect |
| 129. C53 | #7207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276329 | 2 |
| #20274515 | 2 |
| C53×#2115 | 2 |
| #7207 | 53 |