Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22598999 | C2 | semidirect |
| 3. #22590560 | C2 | semidirect |
| 4. #22590517 | C2 | semidirect |
| 5. #22590422 | C2 | semidirect |
| 7. #22590233 | C2 | semidirect |
| 8. C71×#2166 | C2 | semidirect |
| 13. #17986401 | C22 | semidirect |
| 14. #17986379 | C22 | semidirect |
| 22. #17986107 | C22 | semidirect |
| 26. #17985822 | C22 | semidirect |
| 27. #17985816 | C22 | semidirect |
| 30. #364×C71 | C22 | semidirect |
| 32. #347×C71 | C22 | semidirect |
| 168. #2166 | D71 | semidirect |
| 169. C71 | #33693 | semidirect |
| 189. #364 | C2×D71 | semidirect |
| 193. #347 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598999 | 2 |
| #22597244 | 2 |
| #22590560 | 2 |
| #22590517 | 2 |
| #22590422 | 2 |
| #22590293 | 2 |
| #22590233 | 2 |
| C71×#2166 | 2 |
| #33693 | 71 |