Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
938 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 155 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. #22599345 | C2 | semidirect |
| 3. #22598889 | C2 | semidirect |
| 4. #22587659 | C2 | semidirect |
| 5. #22586939 | C2 | semidirect |
| 6. C71×#1534 | C2 | semidirect |
| 15. #17986409 | C22 | semidirect |
| 17. #17986393 | C22 | semidirect |
| 18. #17986359 | C22 | semidirect |
| 24. #17985738 | C22 | semidirect |
| 27. #330×C71 | C22 | semidirect |
| 156. #1534 | D71 | semidirect |
| 158. C71 | #19006 | semidirect |
| 178. #330 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986747 | 2 |
| #22599345 | 2 |
| #22598889 | 2 |
| #22587659 | 2 |
| #22586939 | 2 |
| C71×#1534 | 2 |
| #19006 | 71 |