Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
514 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 514 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 |
|---|---|---|
| 2. #22597469 | C2 | semidirect |
| 3. #22589168 | C2 | semidirect |
| 4. C4×#14556056 | C2 | semidirect |
| 5. #22586756 | C2 | semidirect |
| 6. #22586231 | C2 | semidirect |
| 7. C71×#1276 | C2 | semidirect |
| 11. #17986295 | C4 | semidirect |
| 12. #17986290 | C4 | semidirect |
| 13. #17986200 | C4 | semidirect |
| 14. #17986195 | C4 | semidirect |
| 179. Dic142 | #104 | semidirect |
| 223. #1276 | D71 | semidirect |
| 224. C71 | #8970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598401 | 2 |
| #22597469 | 2 |
| #22589168 | 2 |
| C4×#14556056 | 2 |
| #22586756 | 2 |
| #22586231 | 2 |
| C71×#1276 | 2 |
| #8970 | 71 |