Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
222 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 8. #16811546 | C4 | semidirect |
| 12. #16810444 | C4 | semidirect |
| 14. C53×#364 | C4 | semidirect |
| 107. #364 | #6157 | semidirect |
| 108. C53 | #7271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#364 | 2 |
| #20290652 | 2 |
| #364×D53 | 2 |
| #7271 | 53 |