Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
418 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 2. #22612075 | C2 | semidirect |
| 3. #22609327 | C2 | semidirect |
| 4. #22607977 | C2 | semidirect |
| 5. #22607893 | C2 | semidirect |
| 6. #22607887 | C2 | semidirect |
| 7. C73×#2240 | C2 | semidirect |
| 17. C4⋊#11924003 | C22 | semidirect |
| 19. #17988340 | C22 | semidirect |
| 21. #500×C73 | C22 | semidirect |
| 24. C4×C16×C73 | C22 | semidirect |
| 151. #2240 | D73 | semidirect |
| 157. C73 | #12372 | semidirect |
| 160. #500 | C2×D73 | semidirect |
| 172. C4×C16 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621606 | 2 |
| #22612075 | 2 |
| #22609327 | 2 |
| #22607977 | 2 |
| #22607893 | 2 |
| #22607887 | 2 |
| C73×#2240 | 2 |
| #12372 | 73 |