Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
654 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20285720 | C2 | semidirect |
| 2. #20284814 | C2 | semidirect |
| 4. #20275659 | C2 | semidirect |
| 5. #20273312 | C2 | semidirect |
| 6. #20272572 | C2 | semidirect |
| 7. C53×#1490 | C2 | semidirect |
| 39. #13133217 | D4 | semidirect |
| 40. #13133217 | D4 | semidirect |
| 67. #13133128 | D4 | semidirect |
| 79. C4⋊C8×C53 | D4 | semidirect |
| 226. #1490 | D53 | semidirect |
| 260. C53 | #10008 | semidirect |
| 300. C4⋊C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285720 | 2 |
| #20284814 | 2 |
| #20279654 | 2 |
| #20275659 | 2 |
| #20273312 | 2 |
| #20272572 | 2 |
| C53×#1490 | 2 |
| #10008 | 53 |