Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
724 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 724 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 |
|---|---|---|
| 3. #22588264 | C2 | semidirect |
| 4. #22586704 | C2 | semidirect |
| 6. #22586228 | C2 | semidirect |
| 7. C2×#451×C71 | C2 | semidirect |
| 217. C2×#451 | D71 | semidirect |
| 223. C71 | #9989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599142 | 2 |
| C2×#17986138 | 2 |
| #22588264 | 2 |
| #22586704 | 2 |
| #22586699 | 2 |
| #22586228 | 2 |
| C2×#451×C71 | 2 |
| #9989 | 71 |