Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20273468 | C2 | semidirect |
| 4. #20272551 | C2 | semidirect |
| 68. #11719917 | M16 | semidirect |
| 148. C53 | #8837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275510 | 2 |
| C4×#13133134 | 2 |
| #20273468 | 2 |
| #20272551 | 2 |
| C53×#2975 | 2 |
| #8837 | 53 |