Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
600 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20274476 | C2 | semidirect |
| 3. #336×D53 | C2 | semidirect |
| 4. #20272541 | C2 | semidirect |
| 5. #20272535 | C2 | semidirect |
| 6. #20272535 | C2 | semidirect |
| 7. C53×#1272 | C2 | semidirect |
| 223. #1272 | D53 | semidirect |
| 254. C53 | #7690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283019 | 2 |
| #20274476 | 2 |
| #336×D53 | 2 |
| #20272541 | 2 |
| #20272535 | 2 |
| C53×#1272 | 2 |
| #7690 | 53 |