Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
690 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20283743 | C2 | semidirect |
| 3. #20273429 | C2 | semidirect |
| 4. #20273055 | C2 | semidirect |
| 5. #20272572 | C2 | semidirect |
| 6. #20272570 | C2 | semidirect |
| 7. C53×#1555 | C2 | semidirect |
| 51. C4⋊#88322 | D4 | semidirect |
| 68. C4⋊C8×C53 | D4 | semidirect |
| 217. #1555 | D53 | semidirect |
| 250. C53 | #9457 | semidirect |
| 283. C4⋊C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283743 | 2 |
| #20279662 | 2 |
| #20273429 | 2 |
| #20273055 | 2 |
| #20272572 | 2 |
| #20272570 | 2 |
| C53×#1555 | 2 |
| #9457 | 53 |