Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
194 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. C2×#17985839 | C2 | semidirect |
| 4. #22586539 | C2 | semidirect |
| 5. #22586521 | C2 | semidirect |
| 6. #22586520 | C2 | semidirect |
| 78. C22×C71 | Q64 | semidirect |
| 99. C71 | #13695 | semidirect |
| 170. C22 | #17985839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985839 | 2 |
| C22×C71⋊C32 | 2 |
| #22590431 | 2 |
| #22586539 | 2 |
| #22586521 | 2 |
| #22586520 | 2 |
| C71×#2216 | 2 |
| #13695 | 71 |