Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 72 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. #22625355 | C2 | semidirect |
| 4. #22625255 | C2 | semidirect |
| 5. #22624792 | C2 | semidirect |
| 6. #22624787 | C2 | semidirect |
| 26. #17988997 | C4 | semidirect |
| 27. #17988949 | C4 | semidirect |
| 28. #17988947 | C4 | semidirect |
| 34. #501×C73 | C4 | semidirect |
| 197. C73 | #9369 | semidirect |
| 201. #501 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626755 | 2 |
| #22625374 | 2 |
| #22625355 | 2 |
| #22625255 | 2 |
| #22624792 | 2 |
| #22624787 | 2 |
| #22621172 | 2 |
| #9369 | 73 |