Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
558 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22587012 | C2 | semidirect |
| 4. #22586243 | C2 | semidirect |
| 143. C71 | #9393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597364 | 2 |
| #22588332 | 2 |
| #22587012 | 2 |
| #22586243 | 2 |
| C71×#2547 | 2 |
| #9393 | 71 |