Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
386 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20274868 | C2 | semidirect |
| 3. #20273413 | C2 | semidirect |
| 4. #20273228 | C2 | semidirect |
| 6. #20272584 | C2 | semidirect |
| 184. C53 | #10514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286031 | 2 |
| #20274868 | 2 |
| #20273413 | 2 |
| #20273228 | 2 |
| #20273223 | 2 |
| #20272584 | 2 |
| C53×#1551 | 2 |
| #10514 | 53 |