Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
716 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 716 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 |
|---|---|---|
| 4. #20274651 | C2 | semidirect |
| 5. #20274649 | C2 | semidirect |
| 6. #20272582 | C2 | semidirect |
| 7. C53×#1289 | C2 | semidirect |
| 19. #16810544 | C4 | semidirect |
| 20. #16810536 | C4 | semidirect |
| 239. #1289 | D53 | semidirect |
| 271. C53 | #9471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283741 | 2 |
| #20278081 | 2 |
| #20274700 | 2 |
| #20274651 | 2 |
| #20274649 | 2 |
| #20272582 | 2 |
| C53×#1289 | 2 |
| #9471 | 53 |