Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
684 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 684 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 |
|---|---|---|
| 4. #22588019 | C2 | semidirect |
| 5. #22587983 | C2 | semidirect |
| 6. #22587975 | C2 | semidirect |
| 7. #22587936 | C2 | semidirect |
| 160. C71 | #19751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599085 | 2 |
| #22599081 | 2 |
| #22598882 | 2 |
| #22588019 | 2 |
| #22587983 | 2 |
| #22587975 | 2 |
| #22587936 | 2 |
| #22586643 | 2 |
| C71×#3139 | 2 |
| #19751 | 71 |