Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
334 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #22586320 | C2 | semidirect |
| 5. Q8⋊(C71⋊C16) | C2 | semidirect |
| 6. #22586318 | C2 | semidirect |
| 7. C71×Q8⋊C16 | C2 | semidirect |
| 156. Q8⋊C16 | D71 | semidirect |
| 157. C71 | #11639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Q8×D71 | 2 |
| #22590142 | 2 |
| #22590137 | 2 |
| #22586320 | 2 |
| Q8⋊(C71⋊C16) | 2 |
| #22586318 | 2 |
| C71×Q8⋊C16 | 2 |
| #11639 | 71 |