Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
304 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 73 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. Q8×Dic284 | C2 | semidirect |
| 5. #22586397 | C2 | semidirect |
| 6. #22586305 | C2 | semidirect |
| 7. C71×Q8⋊C16 | C2 | semidirect |
| 60. Dic284 | SD16 | semidirect |
| 86. Q8×C71 | SD32 | semidirect |
| 133. Q8⋊C16 | D71 | semidirect |
| 135. C71 | #12354 | semidirect |
| 218. Q8 | #14556073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic284 | 2 |
| #22590564 | 2 |
| #22590381 | 2 |
| #22587700 | 2 |
| #22586397 | 2 |
| #22586305 | 2 |
| C71×Q8⋊C16 | 2 |
| #12354 | 71 |