Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
874 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 874 conjugacy classes of subgroups — too many to draw. Only its 159 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. #22599270 | C2 | semidirect |
| 2. #22599259 | C2 | semidirect |
| 3. #22599079 | C2 | semidirect |
| 4. #22598791 | C2 | semidirect |
| 5. #22588006 | C2 | semidirect |
| 6. #22588004 | C2 | semidirect |
| 7. #22587976 | C2 | semidirect |
| 8. #22587954 | C2 | semidirect |
| 9. #22587942 | C2 | semidirect |
| 10. #22586638 | C2 | semidirect |
| 11. C71×#1715 | C2 | semidirect |
| 18. #17986376 | C22 | semidirect |
| 21. #17986375 | C22 | semidirect |
| 24. #17986349 | C22 | semidirect |
| 26. #17986347 | C22 | semidirect |
| 27. #17986346 | C22 | semidirect |
| 36. #17985720 | C22 | semidirect |
| 37. C8×C71⋊C8 | C22 | semidirect |
| 38. #498×C71 | C22 | semidirect |
| 40. #492×C71 | C22 | semidirect |
| 42. #322×C71 | C22 | semidirect |
| 205. #1715 | D71 | semidirect |
| 209. C71 | #19727 | semidirect |
| 214. #498 | C2×D71 | semidirect |
| 224. #492 | C2×D71 | semidirect |
| 239. #322 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599270 | 2 |
| #22599259 | 2 |
| #22599079 | 2 |
| #22598791 | 2 |
| #22588006 | 2 |
| #22588004 | 2 |
| #22587976 | 2 |
| #22587954 | 2 |
| #22587942 | 2 |
| #22586638 | 2 |
| C71×#1715 | 2 |
| #19727 | 71 |