Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
344 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22590564 | C2 | semidirect |
| 3. #22590478 | C2 | semidirect |
| 4. #22587734 | C2 | semidirect |
| 5. #22586387 | C2 | semidirect |
| 6. #22586302 | C2 | semidirect |
| 7. C71×Q8⋊C16 | C2 | semidirect |
| 143. Q8⋊C16 | D71 | semidirect |
| 145. C71 | #12380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601315 | 2 |
| #22590564 | 2 |
| #22590478 | 2 |
| #22587734 | 2 |
| #22586387 | 2 |
| #22586302 | 2 |
| C71×Q8⋊C16 | 2 |
| #12380 | 71 |