Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
934 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 171 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×#17985802 | C2 | semidirect |
| 9. C22×Dic284 | C4 | semidirect |
| 60. Dic284 | C22⋊C4 | semidirect |
| 112. C22×C71 | #358 | semidirect |
| 135. C71 | #12732 | semidirect |
| 243. C22 | #17985802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic284 | 2 |
| C2×#17985802 | 2 |
| C2×C22⋊(C71⋊C16) | 2 |
| C71×#1808 | 2 |
| #12732 | 71 |