Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
482 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #20274857 | C2 | semidirect |
| 3. #20274830 | C2 | semidirect |
| 4. #20272539 | C2 | semidirect |
| 5. #20272537 | C2 | semidirect |
| 31. D4×Dic53 | C8 | semidirect |
| 224. C53 | #7594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277177 | 2 |
| #20274857 | 2 |
| #20274830 | 2 |
| #20272539 | 2 |
| #20272537 | 2 |
| #20272536 | 2 |
| C53×#1270 | 2 |
| #7594 | 53 |