Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 258 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 |
|---|---|---|
| 1. #20291130 | C2 | semidirect |
| 2. Q8×#11719910 | C2 | semidirect |
| 103. C53 | #33500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291130 | 2 |
| Q8×#11719910 | 2 |
| #20291080 | 2 |
| #20291072 | 2 |
| #20283650 | 2 |
| #33500 | 53 |