Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
308 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 308 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 |
|---|---|---|
| 24. C2×#11924031 | Q8 | semidirect |
| 107. C73 | #13269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626272 | 2 |
| #22626154 | 2 |
| #22624982 | 2 |
| #22624972 | 2 |
| #22618868 | 2 |
| #13269 | 73 |