Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
830 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 111 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×#17986155 | C2 | semidirect |
| 4. C2×#17985735 | C2 | semidirect |
| 6. #22586183 | C2 | semidirect |
| 7. C71×#1446 | C2 | semidirect |
| 252. #1446 | D71 | semidirect |
| 254. C71 | #9965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986155 | 2 |
| C2×#17986138 | 2 |
| #22594268 | 2 |
| C2×#17985735 | 2 |
| C2×#17985732 | 2 |
| #22586183 | 2 |
| C71×#1446 | 2 |
| #9965 | 71 |