Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20286324 | C2 | semidirect |
| 2. #20276982 | C2 | semidirect |
| 3. #20276751 | C2 | semidirect |
| 4. #20274195 | C2 | semidirect |
| 5. #20272681 | C2 | semidirect |
| 6. #20272672 | C2 | semidirect |
| 7. C53×#1360 | C2 | semidirect |
| 13. #16811000 | C22 | semidirect |
| 22. #16810399 | C22 | semidirect |
| 25. C53×C4⋊C16 | C22 | semidirect |
| 26. C53×#334 | C22 | semidirect |
| 109. D424 | D8 | semidirect |
| 177. #1360 | D53 | semidirect |
| 201. C4⋊C16 | C2×D53 | semidirect |
| 204. #334 | C2×D53 | semidirect |
| 206. C53 | #12324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286324 | 2 |
| #20276982 | 2 |
| #20276751 | 2 |
| #20274195 | 2 |
| #20272681 | 2 |
| #20272672 | 2 |
| C53×#1360 | 2 |
| #12324 | 53 |