Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
526 conjugacy classes of subgroups; only the 350 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 350 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. Q8×#11719910 | C2 | semidirect |
| 23. C2×Q8×C53 | C16 | semidirect |
| 75. C53 | #33496 | semidirect |
| 87. C2×Q8 | #11719910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11719910 | 2 |
| #20291072 | 2 |
| C2×Q8×#88322 | 2 |
| #33496 | 53 |