Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 558 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 |
|---|---|---|
| 2. #20283432 | C2 | semidirect |
| 3. #20275540 | C2 | semidirect |
| 4. #20273276 | C2 | semidirect |
| 5. #20272575 | C2 | semidirect |
| 6. #20272545 | C2 | semidirect |
| 7. C53×#1545 | C2 | semidirect |
| 10. #16810999 | C4 | semidirect |
| 11. #16810969 | C4 | semidirect |
| 116. C2×#88322 | D8 | semidirect |
| 192. #1545 | D53 | semidirect |
| 222. C53 | #9293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285633 | 2 |
| #20283432 | 2 |
| #20275540 | 2 |
| #20273276 | 2 |
| #20272575 | 2 |
| #20272545 | 2 |
| C53×#1545 | 2 |
| #9293 | 53 |