Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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. #22590554 | C2 | semidirect |
| 3. #22590114 | C2 | semidirect |
| 4. C2×#17985811 | C2 | semidirect |
| 5. #22589961 | C2 | semidirect |
| 6. C71×#2916 | C2 | semidirect |
| 14. #17985823 | C22 | semidirect |
| 16. #17985781 | C22 | semidirect |
| 20. #430×C71 | C22 | semidirect |
| 132. #2916 | D71 | semidirect |
| 137. C71 | #33657 | semidirect |
| 146. #430 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597988 | 2 |
| #22590554 | 2 |
| #22590114 | 2 |
| C2×#17985811 | 2 |
| #22589961 | 2 |
| C71×#2916 | 2 |
| #33657 | 71 |