Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 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. #22590134 | C2 | semidirect |
| 3. #22590087 | C2 | semidirect |
| 4. C2×#17985808 | C2 | semidirect |
| 5. #22589961 | C2 | semidirect |
| 6. #22586438 | C2 | semidirect |
| 7. C71×#1815 | C2 | semidirect |
| 182. #1815 | D71 | semidirect |
| 184. C71 | #13391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598060 | 2 |
| #22590134 | 2 |
| #22590087 | 2 |
| C2×#17985808 | 2 |
| #22589961 | 2 |
| #22586438 | 2 |
| C71×#1815 | 2 |
| #13391 | 71 |