Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20276982 | C2 | semidirect |
| 2. #20276750 | C2 | semidirect |
| 3. #20274194 | C2 | semidirect |
| 4. #20272758 | C2 | semidirect |
| 5. #20272682 | C2 | semidirect |
| 6. #20272673 | C2 | semidirect |
| 7. C53×#3273 | C2 | semidirect |
| 11. #16811000 | C22 | semidirect |
| 13. C4⋊#11719908 | C22 | semidirect |
| 15. #16810399 | C22 | semidirect |
| 16. #16810374 | C22 | semidirect |
| 90. D8×C53 | D8 | semidirect |
| 173. #3273 | D53 | semidirect |
| 206. C53 | #12324 | semidirect |
| 275. D8 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276982 | 2 |
| #20276750 | 2 |
| #20274194 | 2 |
| #20272758 | 2 |
| #20272682 | 2 |
| #20272673 | 2 |
| C53×#3273 | 2 |
| #12324 | 53 |