Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
218 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20273533 | C2 | semidirect |
| 4. #20272780 | C2 | semidirect |
| 5. #20272686 | C2 | semidirect |
| 6. #20272635 | C2 | semidirect |
| 63. Dic212 | M16 | semidirect |
| 125. C53 | #12080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276579 | 2 |
| #20273629 | 2 |
| #20273533 | 2 |
| #20272780 | 2 |
| #20272686 | 2 |
| #20272635 | 2 |
| C53×#1333 | 2 |
| #12080 | 53 |