Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
504 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20273053 | C2 | semidirect |
| 2. #20272659 | C2 | semidirect |
| 3. #20272647 | C2 | semidirect |
| 53. C2×D4×C53 | M16 | semidirect |
| 75. C42×C53 | M16 | semidirect |
| 163. C53 | #11533 | semidirect |
| 200. C2×D4 | #11719917 | semidirect |
| 224. C42 | #11719917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20273053 | 2 |
| #20272659 | 2 |
| #20272647 | 2 |
| C53×#2328 | 2 |
| #11533 | 53 |