Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
508 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 508 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. #22591520 | C2 | semidirect |
| 3. #22587065 | C2 | semidirect |
| 6. #22586205 | C2 | semidirect |
| 7. C71×#1288 | C2 | semidirect |
| 12. #17986379 | C4 | semidirect |
| 13. #17986372 | C4 | semidirect |
| 163. #1288 | D71 | semidirect |
| 164. C71 | #9429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598799 | 2 |
| #22591520 | 2 |
| #22587065 | 2 |
| #22586888 | 2 |
| #22586886 | 2 |
| #22586205 | 2 |
| C71×#1288 | 2 |
| #9429 | 71 |