Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
434 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22609977 | C2 | semidirect |
| 4. #22608061 | C2 | semidirect |
| 5. C73×#1813 | C2 | semidirect |
| 6. C22×C8×D73 | C4 | semidirect |
| 13. #17988615 | C4 | semidirect |
| 16. #17988550 | C4 | semidirect |
| 17. #17988542 | C4 | semidirect |
| 189. #1813 | D73 | semidirect |
| 192. C73 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618623 | 2 |
| #22611573 | 2 |
| #22609977 | 2 |
| #22608061 | 2 |
| C73×#1813 | 2 |
| #12805 | 73 |