Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
520 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22599086 | C2 | semidirect |
| 3. #22590561 | C2 | semidirect |
| 4. #22590508 | C2 | semidirect |
| 5. #22590422 | C2 | semidirect |
| 6. #22590421 | C2 | semidirect |
| 8. #22590230 | C2 | semidirect |
| 9. #22590228 | C2 | semidirect |
| 10. #22590151 | C2 | semidirect |
| 11. C71×#2230 | C2 | semidirect |
| 17. #17986379 | C22 | semidirect |
| 27. #17986105 | C22 | semidirect |
| 31. #17985821 | C22 | semidirect |
| 32. #17985820 | C22 | semidirect |
| 33. #17985816 | C22 | semidirect |
| 34. #17985814 | C22 | semidirect |
| 37. #17985776 | C22 | semidirect |
| 38. #498×C71 | C22 | semidirect |
| 40. #365×C71 | C22 | semidirect |
| 41. #364×C71 | C22 | semidirect |
| 217. #2230 | D71 | semidirect |
| 224. C71 | #33689 | semidirect |
| 230. #498 | C2×D71 | semidirect |
| 247. #365 | C2×D71 | semidirect |
| 249. #364 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599086 | 2 |
| #22597245 | 2 |
| #22590561 | 2 |
| #22590508 | 2 |
| #22590422 | 2 |
| #22590421 | 2 |
| #22590292 | 2 |
| #22590230 | 2 |
| #22590228 | 2 |
| #22590151 | 2 |
| C71×#2230 | 2 |
| #33689 | 71 |