Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
324 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20274846 | C2 | semidirect |
| 3. #20272728 | C2 | semidirect |
| 5. C53×#2162 | C2 | semidirect |
| 7. #16811025 | C4 | semidirect |
| 8. #16811007 | C4 | semidirect |
| 13. C4×Dic212 | C4 | semidirect |
| 15. C4×D424 | C4 | semidirect |
| 138. #2162 | D53 | semidirect |
| 164. C53 | #11855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285285 | 2 |
| #20274846 | 2 |
| #20272728 | 2 |
| #20272725 | 2 |
| C53×#2162 | 2 |
| #11855 | 53 |