Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 1. #20285228 | C2 | semidirect |
| 3. #20276962 | C2 | semidirect |
| 4. #20276961 | C2 | semidirect |
| 5. #20276956 | C2 | semidirect |
| 6. #20276950 | C2 | semidirect |
| 7. #20276419 | C2 | semidirect |
| 8. #346×D53 | C2 | semidirect |
| 9. C53×#2244 | C2 | semidirect |
| 150. #2244 | D53 | semidirect |
| 183. C53 | #33701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285228 | 2 |
| #20285142 | 2 |
| #20276962 | 2 |
| #20276961 | 2 |
| #20276956 | 2 |
| #20276950 | 2 |
| #20276419 | 2 |
| #346×D53 | 2 |
| C53×#2244 | 2 |
| #33701 | 53 |