Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
252 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 58 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. #16811491 | C4 | semidirect |
| 7. C22×#11719908 | C4 | semidirect |
| 9. C2×M32×C53 | C4 | semidirect |
| 82. C2×M32 | #6157 | semidirect |
| 88. C53 | #7228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290597 | 2 |
| #20276330 | 2 |
| #7228 | 53 |