Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 3. #22609734 | C2 | semidirect |
| 4. #22608052 | C2 | semidirect |
| 5. C73×#1392 | C2 | semidirect |
| 7. C22×#11924011 | C4 | semidirect |
| 11. #17988613 | C4 | semidirect |
| 13. #17988550 | C4 | semidirect |
| 15. #17988545 | C4 | semidirect |
| 16. #17988378 | C4 | semidirect |
| 17. #17988375 | C4 | semidirect |
| 146. #1392 | D73 | semidirect |
| 148. C73 | #12624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618637 | 2 |
| #22611573 | 2 |
| #22609734 | 2 |
| #22608052 | 2 |
| C73×#1392 | 2 |
| #12624 | 73 |