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 |
| 5. C2×#17985740 | C2 | semidirect |
| 6. #22586222 | C2 | semidirect |
| 7. C71×#1295 | C2 | semidirect |
| 11. #17986364 | C4 | semidirect |
| 224. #1295 | D71 | 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×#17986364 | 2 |
| #22591525 | 2 |
| #22589164 | 2 |
| #22589163 | 2 |
| C2×#17985740 | 2 |
| #22586222 | 2 |
| C71×#1295 | 2 |
| #9002 | 71 |