Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20287851 | C2 | semidirect |
| 2. #20284296 | C2 | semidirect |
| 3. #20276452 | C2 | semidirect |
| 4. #20272817 | C2 | semidirect |
| 5. C53×#2112 | C2 | semidirect |
| 26. C2×Dic212 | D4 | semidirect |
| 28. C2×D424 | D4 | semidirect |
| 39. #13133149 | D4 | semidirect |
| 52. C2×C16×C53 | D4 | semidirect |
| 141. #2112 | D53 | semidirect |
| 163. C53 | #13309 | semidirect |
| 191. C2×C16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287851 | 2 |
| #20284296 | 2 |
| #20276452 | 2 |
| #20272817 | 2 |
| C53×#2112 | 2 |
| #13309 | 53 |