Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
314 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 314 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 |
|---|---|---|
| 1. #22600733 | C2 | semidirect |
| 2. #22590564 | C2 | semidirect |
| 3. #22590381 | C2 | semidirect |
| 5. #22586397 | C2 | semidirect |
| 6. #22586305 | C2 | semidirect |
| 7. C71×D4⋊C16 | C2 | semidirect |
| 89. D4×C71 | SD32 | semidirect |
| 141. D4⋊C16 | D71 | semidirect |
| 142. C71 | #12342 | semidirect |
| 232. D4 | #14556073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22600733 | 2 |
| #22590564 | 2 |
| #22590381 | 2 |
| #22587695 | 2 |
| #22586397 | 2 |
| #22586305 | 2 |
| C71×D4⋊C16 | 2 |
| #12342 | 71 |