Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
466 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22590068 | C2 | semidirect |
| 4. #22590055 | C2 | semidirect |
| 5. #22589944 | C2 | semidirect |
| 6. #22588463 | C2 | semidirect |
| 7. C71×#2145 | C2 | semidirect |
| 13. #17986384 | C4 | semidirect |
| 14. #17986374 | C4 | semidirect |
| 47. C2×C71⋊C16 | D4 | semidirect |
| 63. M32×C71 | D4 | semidirect |
| 177. #2145 | D71 | semidirect |
| 182. C71 | #13215 | semidirect |
| 233. M32 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598827 | 2 |
| C2×#17985813 | 2 |
| #22590068 | 2 |
| #22590055 | 2 |
| #22589944 | 2 |
| #22588463 | 2 |
| C71×#2145 | 2 |
| #13215 | 71 |