Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 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. Q64×D71 | C2 | semidirect |
| 3. Dic2272 | C2 | semidirect |
| 4. #22586557 | C2 | semidirect |
| 5. #22586555 | C2 | semidirect |
| 6. #22586550 | C2 | semidirect |
| 7. C71×SD128 | C2 | semidirect |
| 68. SD128 | D71 | semidirect |
| 70. C71 | #13743 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590646 | 2 |
| Q64×D71 | 2 |
| Dic2272 | 2 |
| #22586557 | 2 |
| #22586555 | 2 |
| #22586550 | 2 |
| C71×SD128 | 2 |
| #13743 | 71 |