Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
548 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. #20277686 | C2 | semidirect |
| 3. #20273276 | C2 | semidirect |
| 4. #20273209 | C2 | semidirect |
| 5. #20273107 | C2 | semidirect |
| 6. #20272575 | C2 | semidirect |
| 7. C53×#1303 | C2 | semidirect |
| 12. #16810829 | C4 | semidirect |
| 13. #16810819 | C4 | semidirect |
| 208. #1303 | D53 | semidirect |
| 238. C53 | #9181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284181 | 2 |
| #20277686 | 2 |
| #20273276 | 2 |
| #20273209 | 2 |
| #20273107 | 2 |
| #20272575 | 2 |
| C53×#1303 | 2 |
| #9181 | 53 |