Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
800 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 800 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. #22589318 | C2 | semidirect |
| 3. #22589167 | C2 | semidirect |
| 4. #22587073 | C2 | semidirect |
| 5. C71×#1561 | C2 | semidirect |
| 6. #17986747 | C4 | semidirect |
| 145. #1561 | D71 | semidirect |
| 147. C71 | #8532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602740 | 2 |
| #22589318 | 2 |
| #22589167 | 2 |
| #22587073 | 2 |
| C71×#1561 | 2 |
| #8532 | 71 |