Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
222 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 35. #13133163 | C8 | semidirect |
| 122. C53 | #12044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290303 | 2 |
| Q16×#88324 | 2 |
| #20289749 | 2 |
| #20289672 | 2 |
| #20289671 | 2 |
| #20289626 | 2 |
| #20276571 | 2 |
| #12044 | 53 |