Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
500 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22609718 | C2 | semidirect |
| 3. #22608246 | C2 | semidirect |
| 4. #22607953 | C2 | semidirect |
| 5. #22607951 | C2 | semidirect |
| 6. #22607928 | C2 | semidirect |
| 7. C73×#1343 | C2 | semidirect |
| 8. C2×#14556578 | C4 | semidirect |
| 13. #17988500 | C4 | semidirect |
| 16. #17988495 | C4 | semidirect |
| 19. #17988454 | C4 | semidirect |
| 227. #1343 | D73 | semidirect |
| 228. C73 | #11730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22615788 | 2 |
| #22609718 | 2 |
| #22608246 | 2 |
| #22607953 | 2 |
| #22607951 | 2 |
| #22607928 | 2 |
| C73×#1343 | 2 |
| #11730 | 73 |