Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
300 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20274116 | C2 | semidirect |
| 5. #20272693 | C2 | semidirect |
| 6. #20272679 | C2 | semidirect |
| 7. C53×#2227 | C2 | semidirect |
| 125. #2227 | D53 | semidirect |
| 151. C53 | #12385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287725 | 2 |
| #20276940 | 2 |
| #20274116 | 2 |
| #20272762 | 2 |
| #20272693 | 2 |
| #20272679 | 2 |
| C53×#2227 | 2 |
| #12385 | 53 |