Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20283856 | C2 | semidirect |
| 3. #20275642 | C2 | semidirect |
| 4. #20273428 | C2 | semidirect |
| 5. #20273238 | C2 | semidirect |
| 6. #20272584 | C2 | semidirect |
| 7. C53×#1285 | C2 | semidirect |
| 10. #16811012 | C4 | semidirect |
| 11. #16810988 | C4 | semidirect |
| 215. #1285 | D53 | semidirect |
| 248. C53 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285735 | 2 |
| #20283856 | 2 |
| #20275642 | 2 |
| #20273428 | 2 |
| #20273238 | 2 |
| #20272584 | 2 |
| C53×#1285 | 2 |
| #9378 | 53 |