Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
612 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #22589284 | C2 | semidirect |
| 4. #22586853 | C2 | semidirect |
| 5. #22586234 | C2 | semidirect |
| 6. #22586195 | C2 | semidirect |
| 11. #17986279 | C4 | semidirect |
| 12. #17986204 | C4 | semidirect |
| 31. #14556128 | C2×C4 | semidirect |
| 32. #14556128 | C2×C4 | semidirect |
| 46. C4⋊(C71⋊C8) | C2×C4 | semidirect |
| 193. C71 | #9323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598439 | 2 |
| #22590701 | 2 |
| #22589284 | 2 |
| #22586853 | 2 |
| #22586234 | 2 |
| #22586195 | 2 |
| C71×#1490 | 2 |
| #9323 | 71 |