Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
706 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20283755 | C2 | semidirect |
| 3. #20274704 | C2 | semidirect |
| 4. #20273383 | C2 | semidirect |
| 5. #20272617 | C2 | semidirect |
| 6. #20272616 | C2 | semidirect |
| 7. C53×#1545 | C2 | semidirect |
| 45. C4⋊#88322 | D4 | semidirect |
| 62. C4⋊C8×C53 | D4 | semidirect |
| 194. #1545 | D53 | semidirect |
| 222. C53 | #9405 | semidirect |
| 254. C4⋊C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283755 | 2 |
| #20279662 | 2 |
| #20274704 | 2 |
| #20273383 | 2 |
| #20272617 | 2 |
| #20272616 | 2 |
| C53×#1545 | 2 |
| #9405 | 53 |