Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
252 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 5. #16810380 | C4 | semidirect |
| 7. C2×M32×C53 | C4 | semidirect |
| 8. C22×C16×C53 | C4 | semidirect |
| 82. C2×M32 | Dic53 | semidirect |
| 83. C22×C16 | Dic53 | semidirect |
| 88. C53 | #7228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274761 | 2 |
| C53×#2113 | 2 |
| #7228 | 53 |