Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
248 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 1. #20289651 | C2 | semidirect |
| 25. C2×D4×C53 | C16 | semidirect |
| 100. C53 | #7056 | semidirect |
| 118. C2×D4 | #11719910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289651 | 2 |
| #20275510 | 2 |
| #7056 | 53 |