Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
382 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 116 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. #22626154 | C2 | semidirect |
| 4. C2×#17989480 | C2 | semidirect |
| 5. #22624982 | C2 | semidirect |
| 6. #22624979 | C2 | semidirect |
| 9. #17989646 | C4 | semidirect |
| 15. #17989486 | C4 | semidirect |
| 150. C73 | #12618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626900 | 2 |
| #22626175 | 2 |
| #22626154 | 2 |
| C2×#17989480 | 2 |
| #22624982 | 2 |
| #22624979 | 2 |
| #22609774 | 2 |
| #12618 | 73 |