Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
566 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 566 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. C2×#17985813 | C2 | semidirect |
| 3. #22590057 | C2 | semidirect |
| 4. #22588219 | C2 | semidirect |
| 5. C2×#364×C71 | C2 | semidirect |
| 10. #17986376 | C4 | semidirect |
| 37. #14556064 | D4 | semidirect |
| 38. #14556062 | D4 | semidirect |
| 133. C2×#364 | D71 | semidirect |
| 137. C71 | #13261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986376 | 2 |
| C2×#17985813 | 2 |
| #22590057 | 2 |
| #22588219 | 2 |
| C2×#364×C71 | 2 |
| #13261 | 71 |