Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1220 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1220 conjugacy classes of subgroups — too many to draw. Only its 271 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. #22596804 | C2 | semidirect |
| 3. #22590011 | C2 | semidirect |
| 4. #22590003 | C2 | semidirect |
| 5. C71×#2884 | C2 | semidirect |
| 6. C2×#14556174 | C4 | semidirect |
| 11. #17986573 | C4 | semidirect |
| 14. C2×#14556117 | C4 | semidirect |
| 16. #41×Dic71 | C4 | semidirect |
| 18. #17985973 | C22 | semidirect |
| 19. #17985793 | C22 | semidirect |
| 20. #17985791 | C22 | semidirect |
| 24. #410×C71 | C22 | semidirect |
| 184. #2884 | D71 | semidirect |
| 187. C71 | #33362 | semidirect |
| 204. #410 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602134 | 2 |
| #22596804 | 2 |
| #22590011 | 2 |
| #22590003 | 2 |
| C71×#2884 | 2 |
| #33362 | 71 |