Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
442 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 123 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×#17985829 | C2 | semidirect |
| 3. C2×#17985813 | C2 | semidirect |
| 4. #22589250 | C2 | semidirect |
| 5. C71×#2108 | C2 | semidirect |
| 10. C2×D1136 | C4 | semidirect |
| 121. #2108 | D71 | semidirect |
| 123. C71 | #13245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1136 | 2 |
| C2×#17985829 | 2 |
| C2×#17985813 | 2 |
| #22589250 | 2 |
| C71×#2108 | 2 |
| #13245 | 71 |