Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
286 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 286 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 |
|---|---|---|
| 2. #20276988 | C2 | semidirect |
| 4. #20272772 | C2 | semidirect |
| 5. #20272679 | C2 | semidirect |
| 7. C53×#2227 | C2 | semidirect |
| 121. #2227 | D53 | semidirect |
| 147. C53 | #12398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287109 | 2 |
| #20276988 | 2 |
| #20274111 | 2 |
| #20272772 | 2 |
| #20272679 | 2 |
| #20272669 | 2 |
| C53×#2227 | 2 |
| #12398 | 53 |