Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
622 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 351 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. #22590134 | C2 | semidirect |
| 4. C2×#17985828 | C2 | semidirect |
| 80. C71 | #33414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986416 | 2 |
| #22596951 | 2 |
| #22590134 | 2 |
| C2×#17985828 | 2 |
| C71×#2916 | 2 |
| #33414 | 71 |