Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 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. #20287817 | C2 | semidirect |
| 3. C2×#16810433 | C2 | semidirect |
| 4. #20274771 | C2 | semidirect |
| 5. #20272828 | C2 | semidirect |
| 6. #20272814 | C2 | semidirect |
| 7. C53×#2143 | C2 | semidirect |
| 14. #16810895 | C4 | semidirect |
| 15. #16810890 | C4 | semidirect |
| 176. #2143 | D53 | semidirect |
| 205. C53 | #13070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287817 | 2 |
| #20284431 | 2 |
| C2×#16810433 | 2 |
| #20274771 | 2 |
| #20272828 | 2 |
| #20272814 | 2 |
| C53×#2143 | 2 |
| #13070 | 53 |