Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
410 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 148 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. #22626142 | C2 | semidirect |
| 4. #22624982 | C2 | semidirect |
| 8. C2×#14556665 | C4 | semidirect |
| 11. C22×#11924031 | C4 | semidirect |
| 13. #17989483 | C4 | semidirect |
| 112. C73 | #12613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989645 | 2 |
| #22626167 | 2 |
| #22626142 | 2 |
| #22624982 | 2 |
| #22609734 | 2 |
| #12613 | 73 |