Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
498 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 498 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. #22597479 | C2 | semidirect |
| 3. #22589267 | C2 | semidirect |
| 4. #22587053 | C2 | semidirect |
| 5. #22586209 | C2 | semidirect |
| 6. #22586196 | C2 | semidirect |
| 7. C71×#1509 | C2 | semidirect |
| 9. #17986389 | C4 | semidirect |
| 10. #17986365 | C4 | semidirect |
| 220. #1509 | D71 | semidirect |
| 223. C71 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599355 | 2 |
| #22597479 | 2 |
| #22589267 | 2 |
| #22587053 | 2 |
| #22586209 | 2 |
| #22586196 | 2 |
| C71×#1509 | 2 |
| #9378 | 71 |