Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
286 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 9. C4⋊#11719910 | C4 | semidirect |
| 13. C4×#11719908 | C4 | semidirect |
| 15. C4×C16×C53 | C4 | semidirect |
| 44. C4⋊#6157 | C16 | semidirect |
| 124. C4×C16 | #6157 | semidirect |
| 126. C53 | #7167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C4⋊C16) | 2 |
| C8×C4⋊#6157 | 2 |
| C4×C16×D53 | 2 |
| #7167 | 53 |