Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
678 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20285838 | C2 | semidirect |
| 3. #20283072 | C2 | semidirect |
| 4. #20275543 | C2 | semidirect |
| 5. #20273386 | C2 | semidirect |
| 6. #20273382 | C2 | semidirect |
| 7. C53×#1276 | C2 | semidirect |
| 105. C42×C53 | D8 | semidirect |
| 192. #1276 | D53 | semidirect |
| 220. C53 | #10284 | semidirect |
| 309. C42 | D424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285838 | 2 |
| #20285635 | 2 |
| #20283072 | 2 |
| #20275543 | 2 |
| #20273386 | 2 |
| #20273382 | 2 |
| C53×#1276 | 2 |
| #10284 | 53 |