Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
274 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 10. C8×#88324 | C4 | semidirect |
| 13. #16810444 | C4 | semidirect |
| 15. C53×#364 | C4 | semidirect |
| 19. #13133288 | C8 | semidirect |
| 21. #13133286 | C8 | semidirect |
| 113. #364 | #6157 | semidirect |
| 117. C53 | #7179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290517 | 2 |
| C8×D53⋊C8 | 2 |
| #364×D53 | 2 |
| #7179 | 53 |