Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
410 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20276518 | C2 | semidirect |
| 3. #20272757 | C2 | semidirect |
| 4. C53×#1566 | C2 | semidirect |
| 13. C4⋊#11719908 | C22 | semidirect |
| 19. C53×#334 | C22 | semidirect |
| 131. #1566 | D53 | semidirect |
| 152. #334 | C2×D53 | semidirect |
| 153. C53 | #11959 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811007 | 2 |
| #20276518 | 2 |
| #20272757 | 2 |
| C53×#1566 | 2 |
| #11959 | 53 |