Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1318 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 191 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 |
|---|---|---|
| 1. C2×#17986611 | C2 | semidirect |
| 4. #22589487 | C2 | semidirect |
| 5. #22589425 | C2 | semidirect |
| 6. #22588694 | C2 | semidirect |
| 7. #22588650 | C2 | semidirect |
| 8. C71×#1818 | C2 | semidirect |
| 12. C2×#14556128 | C22 | semidirect |
| 14. C2×#14556120 | C22 | semidirect |
| 17. C2×C4×Dic142 | C22 | semidirect |
| 20. C2×#14556053 | C22 | semidirect |
| 26. #17985762 | C22 | semidirect |
| 29. #336×C71 | C22 | semidirect |
| 30. #336×C71 | C22 | semidirect |
| 194. #1818 | D71 | semidirect |
| 195. C71 | #23942 | semidirect |
| 216. #336 | C2×D71 | semidirect |
| 217. #336 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986611 | 2 |
| C2×#17986152 | 2 |
| #22590920 | 2 |
| #22589487 | 2 |
| #22589425 | 2 |
| #22588694 | 2 |
| #22588650 | 2 |
| C71×#1818 | 2 |
| #23942 | 71 |