Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
488 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22587057 | C2 | semidirect |
| 5. #22586213 | C2 | semidirect |
| 6. #22586211 | C2 | semidirect |
| 7. C71×#1556 | C2 | semidirect |
| 154. #1556 | D71 | semidirect |
| 158. C71 | #9421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598797 | 2 |
| #22597410 | 2 |
| #22587057 | 2 |
| #22586974 | 2 |
| #22586213 | 2 |
| #22586211 | 2 |
| C71×#1556 | 2 |
| #9421 | 71 |