Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
414 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22588478 | C2 | semidirect |
| 4. #22586215 | C2 | semidirect |
| 5. C2×#335×C71 | C2 | semidirect |
| 139. C2×#335 | D71 | semidirect |
| 142. C71 | #8688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597053 | 2 |
| #22588478 | 2 |
| #22587015 | 2 |
| #22586215 | 2 |
| C2×#335×C71 | 2 |
| #8688 | 71 |