Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
460 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22588143 | C2 | semidirect |
| 4. #22586470 | C2 | semidirect |
| 6. C2×#14556135 | C4 | semidirect |
| 10. #17986023 | C4 | semidirect |
| 12. #17985966 | C4 | semidirect |
| 15. C2×C4×C71⋊C8 | C4 | semidirect |
| 21. #356×C71 | C4 | semidirect |
| 22. #355×C71 | C4 | semidirect |
| 157. C71 | #12633 | semidirect |
| 170. #356 | Dic71 | semidirect |
| 171. #355 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597052 | 2 |
| #22590005 | 2 |
| #22588143 | 2 |
| #22586470 | 2 |
| C71×#2132 | 2 |
| #12633 | 71 |