Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
468 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 2. #22597415 | C2 | semidirect |
| 3. #22587060 | C2 | semidirect |
| 4. #22586681 | C2 | semidirect |
| 5. #22586251 | C2 | semidirect |
| 6. #22586202 | C2 | semidirect |
| 7. C71×#1486 | C2 | semidirect |
| 183. #1486 | D71 | semidirect |
| 187. C71 | #9529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598431 | 2 |
| #22597415 | 2 |
| #22587060 | 2 |
| #22586681 | 2 |
| #22586251 | 2 |
| #22586202 | 2 |
| C71×#1486 | 2 |
| #9529 | 71 |