Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
542 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22591525 | C2 | semidirect |
| 4. C2×#17985740 | C2 | semidirect |
| 5. #22586222 | C2 | semidirect |
| 6. #22586221 | C2 | semidirect |
| 10. #17986363 | C4 | semidirect |
| 225. C71 | #9002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986363 | 2 |
| #22591525 | 2 |
| #22589165 | 2 |
| C2×#17985740 | 2 |
| #22586222 | 2 |
| #22586221 | 2 |
| C71×#1961 | 2 |
| #9002 | 71 |