Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
766 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22589137 | C2 | semidirect |
| 3. #22587033 | C2 | semidirect |
| 4. #22586955 | C2 | semidirect |
| 5. #22586952 | C2 | semidirect |
| 6. #22586680 | C2 | semidirect |
| 7. C71×#1552 | C2 | semidirect |
| 225. #1552 | D71 | semidirect |
| 230. C71 | #8458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602194 | 2 |
| #22589137 | 2 |
| #22587033 | 2 |
| #22586955 | 2 |
| #22586952 | 2 |
| #22586680 | 2 |
| C71×#1552 | 2 |
| #8458 | 71 |