Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
400 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22600100 | C2 | semidirect |
| 2. #22590590 | C2 | semidirect |
| 3. #22590381 | C2 | semidirect |
| 4. #22587695 | C2 | semidirect |
| 5. #22586387 | C2 | semidirect |
| 6. #22586305 | C2 | semidirect |
| 7. C71×D4⋊C16 | C2 | semidirect |
| 69. Dic284 | D8 | semidirect |
| 159. D4⋊C16 | D71 | semidirect |
| 160. C71 | #12317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22600100 | 2 |
| #22590590 | 2 |
| #22590381 | 2 |
| #22587695 | 2 |
| #22586387 | 2 |
| #22586305 | 2 |
| C71×D4⋊C16 | 2 |
| #12317 | 71 |