Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
714 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20273042 | C2 | semidirect |
| 2. #20272645 | C2 | semidirect |
| 3. #20272643 | C2 | semidirect |
| 58. C24×C53 | M16 | semidirect |
| 83. C22×C4×C53 | M16 | semidirect |
| 213. C53 | #11502 | semidirect |
| 253. C24 | #11719917 | semidirect |
| 279. C22×C4 | #11719917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20273042 | 2 |
| #20272645 | 2 |
| #20272643 | 2 |
| C53×#2308 | 2 |
| #11502 | 53 |