Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1114 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1114 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 |
|---|---|---|
| 2. C2×#17986416 | C2 | semidirect |
| 3. #22590067 | C2 | semidirect |
| 4. C2×#17985805 | C2 | semidirect |
| 5. C71×#2916 | C2 | semidirect |
| 13. C2×#14556068 | C22 | semidirect |
| 14. C22×C71⋊C16 | C22 | semidirect |
| 15. #17985805 | C22 | semidirect |
| 16. #17985805 | C22 | semidirect |
| 20. C2×#108×C71 | C22 | semidirect |
| 119. #2916 | D71 | semidirect |
| 122. C71 | #33385 | semidirect |
| 135. C2×#108 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22603114 | 2 |
| C2×#17986416 | 2 |
| #22590067 | 2 |
| C2×#17985805 | 2 |
| C71×#2916 | 2 |
| #33385 | 71 |