Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
400 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 135 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. #20272998 | C2 | semidirect |
| 4. #20272559 | C2 | semidirect |
| 5. C53×#1452 | C2 | semidirect |
| 106. #1452 | D53 | semidirect |
| 128. C53 | #8158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810682 | 2 |
| #20273027 | 2 |
| #20272998 | 2 |
| #20272559 | 2 |
| C53×#1452 | 2 |
| #8158 | 53 |