Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
376 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 113. Q8×C53 | #108 | semidirect |
| 197. C53 | #8909 | semidirect |
| 285. Q8 | #13133288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11719936 | 2 |
| #20290829 | 2 |
| #20290271 | 2 |
| #20290044 | 2 |
| #20289607 | 2 |
| #20289547 | 2 |
| Q8⋊C8×D53 | 2 |
| #8909 | 53 |