Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20277189 | C2 | semidirect |
| 4. #20273145 | C2 | semidirect |
| 5. #20272618 | C2 | semidirect |
| 6. #20272547 | C2 | semidirect |
| 10. #16810905 | C4 | semidirect |
| 11. #16810820 | C4 | semidirect |
| 118. C4×Dic53 | SD16 | semidirect |
| 224. C53 | #9238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284742 | 2 |
| #20277189 | 2 |
| #20275544 | 2 |
| #20273145 | 2 |
| #20272618 | 2 |
| #20272547 | 2 |
| C53×#1502 | 2 |
| #9238 | 53 |