Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
624 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22611625 | C2 | semidirect |
| 4. #22611584 | C2 | semidirect |
| 6. #22608054 | C2 | semidirect |
| 7. C73×#1395 | C2 | semidirect |
| 9. C2×#14556624 | C4 | semidirect |
| 10. C22×Dic292 | C4 | semidirect |
| 18. #17988597 | C4 | semidirect |
| 20. #17988584 | C4 | semidirect |
| 244. #1395 | D73 | semidirect |
| 246. C73 | #13096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619228 | 2 |
| #22618412 | 2 |
| #22611625 | 2 |
| #22611584 | 2 |
| #22609904 | 2 |
| #22608054 | 2 |
| C73×#1395 | 2 |
| #13096 | 73 |