Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
494 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #20275536 | C2 | semidirect |
| 5. #20272575 | C2 | semidirect |
| 6. #20272545 | C2 | semidirect |
| 7. C53×#1546 | C2 | semidirect |
| 10. #16811026 | C4 | semidirect |
| 11. #16810971 | C4 | semidirect |
| 179. #1546 | D53 | semidirect |
| 208. C53 | #9291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285836 | 2 |
| #20283432 | 2 |
| #20275536 | 2 |
| #20273276 | 2 |
| #20272575 | 2 |
| #20272545 | 2 |
| C53×#1546 | 2 |
| #9291 | 53 |