Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
922 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 1. #22598918 | C2 | semidirect |
| 2. #22598769 | C2 | semidirect |
| 3. #22598767 | C2 | semidirect |
| 4. #22587956 | C2 | semidirect |
| 5. #22587954 | C2 | semidirect |
| 6. #22587946 | C2 | semidirect |
| 7. #22587931 | C2 | semidirect |
| 8. C82×D71 | C2 | semidirect |
| 9. C71×#1709 | C2 | semidirect |
| 85. C8×D71 | D8 | semidirect |
| 124. C71⋊C8 | #135 | semidirect |
| 150. #1709 | D71 | semidirect |
| 153. C71 | #19603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598918 | 2 |
| #22598769 | 2 |
| #22598767 | 2 |
| #22587956 | 2 |
| #22587954 | 2 |
| #22587946 | 2 |
| #22587931 | 2 |
| C82×D71 | 2 |
| C71×#1709 | 2 |
| #19603 | 71 |