Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
372 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22587086 | C2 | semidirect |
| 3. C2×#17985749 | C2 | semidirect |
| 6. #22586191 | C2 | semidirect |
| 7. C71×#1283 | C2 | semidirect |
| 161. #1283 | D71 | semidirect |
| 162. C71 | #8607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596985 | 2 |
| #22587086 | 2 |
| C2×#17985749 | 2 |
| #22586728 | 2 |
| #22586725 | 2 |
| #22586191 | 2 |
| C71×#1283 | 2 |
| #8607 | 71 |