Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20286327 | C2 | semidirect |
| 2. #20276981 | C2 | semidirect |
| 3. #20276751 | C2 | semidirect |
| 4. #20274194 | C2 | semidirect |
| 5. #20272759 | C2 | semidirect |
| 6. #20272683 | C2 | semidirect |
| 7. C53×#1330 | C2 | semidirect |
| 14. #16811000 | C22 | semidirect |
| 22. #16810374 | C22 | semidirect |
| 25. C53×C4⋊C16 | C22 | semidirect |
| 26. C53×#346 | C22 | semidirect |
| 108. D424 | D8 | semidirect |
| 179. #1330 | D53 | semidirect |
| 201. C4⋊C16 | C2×D53 | semidirect |
| 203. #346 | 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 |
|---|---|
| #20286327 | 2 |
| #20276981 | 2 |
| #20276751 | 2 |
| #20274194 | 2 |
| #20272759 | 2 |
| #20272683 | 2 |
| C53×#1330 | 2 |
| #12324 | 53 |