Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
306 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22611536 | C2 | semidirect |
| 4. #22610711 | C2 | semidirect |
| 5. #22608047 | C2 | semidirect |
| 6. #22608036 | C2 | semidirect |
| 13. #17988403 | C4 | semidirect |
| 14. #17988400 | C4 | semidirect |
| 147. C73 | #13156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611680 | 2 |
| C2×#17988397 | 2 |
| #22611536 | 2 |
| #22610711 | 2 |
| #22608047 | 2 |
| #22608036 | 2 |
| C73×#1976 | 2 |
| #13156 | 73 |