Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22600771 | C2 | semidirect |
| 2. #22590564 | C2 | semidirect |
| 3. #22590381 | C2 | semidirect |
| 5. #22586394 | C2 | semidirect |
| 6. #22586305 | C2 | semidirect |
| 7. C71×D4⋊C16 | C2 | semidirect |
| 141. D4⋊C16 | D71 | semidirect |
| 142. C71 | #12341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22600771 | 2 |
| #22590564 | 2 |
| #22590381 | 2 |
| #22587695 | 2 |
| #22586394 | 2 |
| #22586305 | 2 |
| C71×D4⋊C16 | 2 |
| #12341 | 71 |