Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
364 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #20272668 | C2 | semidirect |
| 4. #20272667 | C2 | semidirect |
| 5. C53×#1328 | C2 | semidirect |
| 125. #1328 | D53 | semidirect |
| 144. C53 | #11458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283276 | 2 |
| #349×D53 | 2 |
| #20272668 | 2 |
| #20272667 | 2 |
| C53×#1328 | 2 |
| #11458 | 53 |