Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1382 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 267 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. #22596975 | C2 | semidirect |
| 3. #22588421 | C2 | semidirect |
| 4. #22588330 | C2 | semidirect |
| 6. #100×Dic71 | C2 | semidirect |
| 16. #17986022 | C22 | semidirect |
| 19. M16×Dic71 | C22 | semidirect |
| 20. #17985767 | C22 | semidirect |
| 150. C71 | #20729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986474 | 2 |
| #22596975 | 2 |
| #22588421 | 2 |
| #22588330 | 2 |
| #22588261 | 2 |
| #100×Dic71 | 2 |
| C71×#1783 | 2 |
| #20729 | 71 |