Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
874 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 874 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20274477 | C2 | semidirect |
| 3. #20272535 | C2 | semidirect |
| 4. C53×#1749 | C2 | semidirect |
| 15. #16810378 | C22 | semidirect |
| 19. C53×#336 | C22 | semidirect |
| 186. #1749 | D53 | semidirect |
| 211. #336 | C2×D53 | semidirect |
| 212. C53 | #7626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810525 | 2 |
| #20274477 | 2 |
| #20272535 | 2 |
| C53×#1749 | 2 |
| #7626 | 53 |