Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
212 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 30. Q16×C53 | C16 | semidirect |
| 84. C53 | #12059 | semidirect |
| 99. Q16 | #11719910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11719910 | 2 |
| #20289737 | 2 |
| Q8⋊#11719910 | 2 |
| #20289628 | 2 |
| Q16×#88322 | 2 |
| #12059 | 53 |