Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22597510 | C2 | semidirect |
| 3. #22589172 | C2 | semidirect |
| 4. #22586810 | C2 | semidirect |
| 5. #22586233 | C2 | semidirect |
| 6. #22586231 | C2 | semidirect |
| 7. C71×#1500 | C2 | semidirect |
| 9. #17986409 | C4 | semidirect |
| 10. #17986389 | C4 | semidirect |
| 11. #17986365 | C4 | semidirect |
| 12. #17986358 | C4 | semidirect |
| 219. #1500 | D71 | semidirect |
| 223. C71 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598936 | 2 |
| #22597510 | 2 |
| #22589172 | 2 |
| #22586810 | 2 |
| #22586233 | 2 |
| #22586231 | 2 |
| C71×#1500 | 2 |
| #8997 | 71 |