Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
392 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 3. #22624868 | C2 | semidirect |
| 4. #22624867 | C2 | semidirect |
| 166. C73 | #11441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626159 | 2 |
| #22626156 | 2 |
| #22624868 | 2 |
| #22624867 | 2 |
| C2×#17988612 | 2 |
| #11441 | 73 |