Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
334 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 3. #20289682 | C2 | semidirect |
| 4. Q8⋊#11719910 | C2 | semidirect |
| 162. C53 | #11639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291079 | 2 |
| #20291074 | 2 |
| #20289682 | 2 |
| Q8⋊#11719910 | 2 |
| C8×Q8×D53 | 2 |
| #11639 | 53 |