Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
338 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22588513 | C2 | semidirect |
| 5. #22586438 | C2 | semidirect |
| 6. #22586423 | C2 | semidirect |
| 7. C71×#1383 | C2 | semidirect |
| 141. #1383 | D71 | semidirect |
| 143. C71 | #13487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985813 | 2 |
| C2×#17985811 | 2 |
| #22589214 | 2 |
| #22588513 | 2 |
| #22586438 | 2 |
| #22586423 | 2 |
| C71×#1383 | 2 |
| #13487 | 71 |