Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 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. #22609981 | C2 | semidirect |
| 4. #22608059 | C2 | semidirect |
| 5. C73×#1812 | C2 | semidirect |
| 6. C22×#11924011 | C4 | semidirect |
| 13. #17988615 | C4 | semidirect |
| 16. #17988550 | C4 | semidirect |
| 17. #17988542 | C4 | semidirect |
| 189. #1812 | D73 | semidirect |
| 191. C73 | #12806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618632 | 2 |
| #22611570 | 2 |
| #22609981 | 2 |
| #22608059 | 2 |
| C73×#1812 | 2 |
| #12806 | 73 |