Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
460 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #22609734 | C2 | semidirect |
| 5. #22609733 | C2 | semidirect |
| 6. #22608060 | C2 | semidirect |
| 7. C73×#1395 | C2 | semidirect |
| 8. C2×#14556599 | C4 | semidirect |
| 15. #17988610 | C4 | semidirect |
| 18. #17988553 | C4 | semidirect |
| 21. C2×C8×Dic73 | C4 | semidirect |
| 22. #17988385 | C4 | semidirect |
| 23. #17988383 | C4 | semidirect |
| 212. #1395 | D73 | semidirect |
| 213. C73 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618639 | 2 |
| #22611614 | 2 |
| #22611594 | 2 |
| #22609734 | 2 |
| #22609733 | 2 |
| #22608060 | 2 |
| C73×#1395 | 2 |
| #12633 | 73 |