Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
522 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20272548 | C2 | semidirect |
| 4. #20272543 | C2 | semidirect |
| 5. C53×#1276 | C2 | semidirect |
| 25. #13133174 | C8 | semidirect |
| 148. #1276 | D53 | semidirect |
| 168. C53 | #8731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133174 | 2 |
| #20273027 | 2 |
| #20272548 | 2 |
| #20272543 | 2 |
| C53×#1276 | 2 |
| #8731 | 53 |