Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. C2×#17985735 | C2 | semidirect |
| 4. #22586705 | C2 | semidirect |
| 5. #22586227 | C2 | semidirect |
| 6. #22586183 | C2 | semidirect |
| 10. #17986327 | C4 | semidirect |
| 11. #17986310 | C4 | semidirect |
| 15. #17986154 | C4 | semidirect |
| 16. #17986137 | C4 | semidirect |
| 241. C71 | #9263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599117 | 2 |
| #22597396 | 2 |
| C2×#17985735 | 2 |
| #22586705 | 2 |
| #22586227 | 2 |
| #22586183 | 2 |
| C71×#1504 | 2 |
| #9263 | 71 |