Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
316 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22590153 | C2 | semidirect |
| 3. #22588094 | C2 | semidirect |
| 4. #22586332 | C2 | semidirect |
| 5. #22586331 | C2 | semidirect |
| 6. #22586324 | C2 | semidirect |
| 7. C71×#1339 | C2 | semidirect |
| 9. #17986399 | C4 | semidirect |
| 10. #17986374 | C4 | semidirect |
| 14. #17986111 | C4 | semidirect |
| 15. #17986110 | C4 | semidirect |
| 157. #1339 | D71 | semidirect |
| 158. C71 | #11770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598985 | 2 |
| #22590153 | 2 |
| #22588094 | 2 |
| #22586332 | 2 |
| #22586331 | 2 |
| #22586324 | 2 |
| C71×#1339 | 2 |
| #11770 | 71 |