Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1128 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 351 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. #22596935 | C2 | semidirect |
| 3. #22590077 | C2 | semidirect |
| 4. C2×#17985810 | C2 | semidirect |
| 5. C71×#3407 | C2 | semidirect |
| 7. #17986816 | C4 | semidirect |
| 9. #17986804 | C4 | semidirect |
| 14. #17986037 | C22 | semidirect |
| 15. C2×#14556060 | C22 | semidirect |
| 16. #17985810 | C22 | semidirect |
| 17. #17985810 | C22 | semidirect |
| 20. C2×M32×C71 | C22 | semidirect |
| 31. #14556150 | C2×C4 | semidirect |
| 33. C2×Dic284 | C2×C4 | semidirect |
| 35. C2×D568 | C2×C4 | semidirect |
| 127. #3407 | D71 | semidirect |
| 131. C71 | #33388 | semidirect |
| 141. C2×M32 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22603114 | 2 |
| #22596935 | 2 |
| #22590077 | 2 |
| C2×#17985810 | 2 |
| C71×#3407 | 2 |
| #33388 | 71 |