Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
646 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 646 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. #22596802 | C2 | semidirect |
| 3. #22589990 | C2 | semidirect |
| 4. #22588313 | C2 | semidirect |
| 5. #22586468 | C2 | semidirect |
| 6. #22586460 | C2 | semidirect |
| 7. C71×#2128 | C2 | semidirect |
| 9. C2×#14556154 | C4 | semidirect |
| 10. C22×#11765853 | C4 | semidirect |
| 18. #17986007 | C4 | semidirect |
| 19. #17985993 | C4 | semidirect |
| 250. #2128 | D71 | semidirect |
| 255. C71 | #13103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597624 | 2 |
| #22596802 | 2 |
| #22589990 | 2 |
| #22588313 | 2 |
| #22586468 | 2 |
| #22586460 | 2 |
| C71×#2128 | 2 |
| #13103 | 71 |