Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
516 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22590075 | C2 | semidirect |
| 3. C2×#17985781 | C2 | semidirect |
| 4. #22586441 | C2 | semidirect |
| 5. C71×#2911 | C2 | semidirect |
| 9. #17986257 | C4 | semidirect |
| 10. #17986252 | C4 | semidirect |
| 24. C2×Dic284 | C2×C4 | semidirect |
| 26. C2×D568 | C2×C4 | semidirect |
| 37. #14556060 | C2×C4 | semidirect |
| 57. #106×C71 | D4 | semidirect |
| 163. #2911 | D71 | semidirect |
| 167. C71 | #13008 | semidirect |
| 217. #106 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597949 | 2 |
| #22590075 | 2 |
| C2×#17985781 | 2 |
| #22586441 | 2 |
| C71×#2911 | 2 |
| #13008 | 71 |