Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
462 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22597256 | C2 | semidirect |
| 3. C2×#17985805 | C2 | semidirect |
| 4. #22590045 | C2 | semidirect |
| 5. #22589236 | C2 | semidirect |
| 6. #22586430 | C2 | semidirect |
| 7. C71×#1389 | C2 | semidirect |
| 12. #17986442 | C4 | semidirect |
| 14. #17986437 | C4 | semidirect |
| 186. #1389 | D71 | semidirect |
| 188. C71 | #13021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601476 | 2 |
| #22597256 | 2 |
| C2×#17985805 | 2 |
| #22590045 | 2 |
| #22589236 | 2 |
| #22586430 | 2 |
| C71×#1389 | 2 |
| #13021 | 71 |