Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
644 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 644 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. #22609865 | C2 | semidirect |
| 4. #22609854 | C2 | semidirect |
| 6. #22607807 | C2 | semidirect |
| 7. C73×#1305 | C2 | semidirect |
| 12. #17988745 | C4 | semidirect |
| 14. #17988728 | C4 | semidirect |
| 256. #1305 | D73 | semidirect |
| 258. C73 | #9519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619168 | 2 |
| #22618981 | 2 |
| #22609865 | 2 |
| #22609854 | 2 |
| #22608472 | 2 |
| #22607807 | 2 |
| C73×#1305 | 2 |
| #9519 | 73 |