Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
386 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22587026 | C2 | semidirect |
| 4. C2×#17985747 | C2 | semidirect |
| 6. #22586191 | C2 | semidirect |
| 7. C71×#1950 | C2 | semidirect |
| 172. #1950 | D71 | semidirect |
| 178. C71 | #10551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598734 | 2 |
| #22587026 | 2 |
| #22587018 | 2 |
| C2×#17985747 | 2 |
| #22586738 | 2 |
| #22586191 | 2 |
| C71×#1950 | 2 |
| #10551 | 71 |