Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
644 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 5. #22588017 | C2 | semidirect |
| 6. #22587986 | C2 | semidirect |
| 7. #22587986 | C2 | semidirect |
| 8. #22587950 | C2 | semidirect |
| 158. C71 | #19732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599501 | 2 |
| #22599493 | 2 |
| #22599085 | 2 |
| #22598721 | 2 |
| #22588017 | 2 |
| #22587986 | 2 |
| #22587950 | 2 |
| C71×#1453 | 2 |
| #19732 | 71 |