Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22610150 | C2 | semidirect |
| 4. #22608060 | C2 | semidirect |
| 11. #17988386 | C4 | semidirect |
| 12. #17988384 | C4 | semidirect |
| 142. C73 | #12975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611616 | 2 |
| #22610315 | 2 |
| #22610150 | 2 |
| #22608060 | 2 |
| C73×#2979 | 2 |
| #12975 | 73 |