Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
834 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22589181 | C2 | semidirect |
| 3. #22587077 | C2 | semidirect |
| 4. #22586934 | C2 | semidirect |
| 5. #22586780 | C2 | semidirect |
| 6. #22586777 | C2 | semidirect |
| 7. C71×#1965 | C2 | semidirect |
| 248. #1965 | D71 | semidirect |
| 253. C71 | #8472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602214 | 2 |
| #22589181 | 2 |
| #22587077 | 2 |
| #22586934 | 2 |
| #22586780 | 2 |
| #22586777 | 2 |
| C71×#1965 | 2 |
| #8472 | 71 |