Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
294 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #16810418 | C4 | semidirect |
| 7. C53×#423 | C4 | semidirect |
| 9. C43×C53 | C4 | semidirect |
| 89. #423 | Dic53 | semidirect |
| 92. C43 | Dic53 | semidirect |
| 95. C53 | #7500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276380 | 2 |
| C53×#1962 | 2 |
| #7500 | 53 |