Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
590 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22598733 | C2 | semidirect |
| 3. #22594450 | C2 | semidirect |
| 4. #22587056 | C2 | semidirect |
| 5. #22586939 | C2 | semidirect |
| 6. #22586233 | C2 | semidirect |
| 7. C71×#1505 | C2 | semidirect |
| 198. #1505 | D71 | semidirect |
| 200. C71 | #10094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599323 | 2 |
| #22598733 | 2 |
| #22594450 | 2 |
| #22587056 | 2 |
| #22586939 | 2 |
| #22586233 | 2 |
| C71×#1505 | 2 |
| #10094 | 71 |