Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
536 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 536 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. #22598990 | C2 | semidirect |
| 2. #22597244 | C2 | semidirect |
| 3. #22590555 | C2 | semidirect |
| 4. #22590517 | C2 | semidirect |
| 5. #22590417 | C2 | semidirect |
| 6. #22590288 | C2 | semidirect |
| 7. #22590240 | C2 | semidirect |
| 8. C71×#2166 | C2 | semidirect |
| 13. #17986401 | C22 | semidirect |
| 14. #17986376 | C22 | semidirect |
| 22. #17986112 | C22 | semidirect |
| 26. #17985822 | C22 | semidirect |
| 27. #17985813 | C22 | semidirect |
| 30. #364×C71 | C22 | semidirect |
| 32. #347×C71 | C22 | semidirect |
| 174. #2166 | D71 | semidirect |
| 175. C71 | #33692 | semidirect |
| 195. #364 | C2×D71 | semidirect |
| 199. #347 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598990 | 2 |
| #22597244 | 2 |
| #22590555 | 2 |
| #22590517 | 2 |
| #22590417 | 2 |
| #22590288 | 2 |
| #22590240 | 2 |
| C71×#2166 | 2 |
| #33692 | 71 |