Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
640 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22596821 | C2 | semidirect |
| 3. #22590031 | C2 | semidirect |
| 4. #22589991 | C2 | semidirect |
| 5. #22588316 | C2 | semidirect |
| 6. #22586469 | C2 | semidirect |
| 7. C71×#1392 | C2 | semidirect |
| 9. C2×#14556156 | C4 | semidirect |
| 10. C22×#11765854 | C4 | semidirect |
| 19. #17986009 | C4 | semidirect |
| 20. #17985996 | C4 | semidirect |
| 252. #1392 | D71 | semidirect |
| 253. C71 | #13098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597628 | 2 |
| #22596821 | 2 |
| #22590031 | 2 |
| #22589991 | 2 |
| #22588316 | 2 |
| #22586469 | 2 |
| C71×#1392 | 2 |
| #13098 | 71 |