Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
542 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 3. C2×#17985741 | C2 | semidirect |
| 4. #22586221 | C2 | semidirect |
| 5. C71×#2382 | C2 | semidirect |
| 8. #17986365 | C4 | semidirect |
| 137. #2382 | D71 | semidirect |
| 141. C71 | #9002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986365 | 2 |
| #22589163 | 2 |
| C2×#17985741 | 2 |
| #22586221 | 2 |
| C71×#2382 | 2 |
| #9002 | 71 |