Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
564 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20286022 | C2 | semidirect |
| 2. #20284806 | C2 | semidirect |
| 3. #20275514 | C2 | semidirect |
| 4. #20273327 | C2 | semidirect |
| 5. #20273326 | C2 | semidirect |
| 6. #20272584 | C2 | semidirect |
| 7. C53×#3109 | C2 | semidirect |
| 210. #3109 | D53 | semidirect |
| 247. C53 | #10026 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286022 | 2 |
| #20284806 | 2 |
| #20275514 | 2 |
| #20273327 | 2 |
| #20273326 | 2 |
| #20272584 | 2 |
| C53×#3109 | 2 |
| #10026 | 53 |