Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
536 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#17986335 | C2 | semidirect |
| 4. #22588418 | C2 | semidirect |
| 5. #22586703 | C2 | semidirect |
| 7. C71×#1298 | C2 | semidirect |
| 200. #1298 | D71 | semidirect |
| 201. C71 | #9994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599147 | 2 |
| C2×#17986335 | 2 |
| C2×#17986313 | 2 |
| #22588418 | 2 |
| #22586703 | 2 |
| #22586699 | 2 |
| C71×#1298 | 2 |
| #9994 | 71 |