Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
302 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 302 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 |
|---|---|---|
| 2. #22590567 | C2 | semidirect |
| 3. #22590382 | C2 | semidirect |
| 4. #22586399 | C2 | semidirect |
| 5. #22586300 | C2 | semidirect |
| 6. D4⋊(C71⋊C16) | C2 | semidirect |
| 7. C71×#1669 | C2 | semidirect |
| 136. #1669 | D71 | semidirect |
| 140. C71 | #12347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22600763 | 2 |
| #22590567 | 2 |
| #22590382 | 2 |
| #22586399 | 2 |
| #22586300 | 2 |
| D4⋊(C71⋊C16) | 2 |
| C71×#1669 | 2 |
| #12347 | 71 |