Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
274 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 274 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. C53×#376 | C4 | semidirect |
| 88. #423 | Dic53 | semidirect |
| 91. #376 | Dic53 | semidirect |
| 94. C53 | #7506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276380 | 2 |
| C53×#1963 | 2 |
| #7506 | 53 |