Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 92 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. #20291074 | C2 | semidirect |
| 2. #20290274 | C2 | semidirect |
| 3. #20289729 | C2 | semidirect |
| 6. #16811544 | C22 | semidirect |
| 10. #16811487 | C22 | semidirect |
| 163. C53 | #11961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291074 | 2 |
| #20290274 | 2 |
| #20289729 | 2 |
| #493×D53 | 2 |
| #11961 | 53 |