Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
174 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 7. D53⋊C32 | C4 | semidirect |
| 12. #16810453 | C4 | semidirect |
| 14. C53×#368 | C4 | semidirect |
| 88. #368 | #6157 | semidirect |
| 91. C53 | #7474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊M64 | 2 |
| C2×#16811550 | 2 |
| #368×D53 | 2 |
| #7474 | 53 |