Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
788 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22599298 | C2 | semidirect |
| 2. #22599260 | C2 | semidirect |
| 3. #22599078 | C2 | semidirect |
| 4. #22598715 | C2 | semidirect |
| 5. #22588006 | C2 | semidirect |
| 6. #22588000 | C2 | semidirect |
| 7. #22587979 | C2 | semidirect |
| 8. #22587946 | C2 | semidirect |
| 9. C71×#1453 | C2 | semidirect |
| 13. #17986397 | C22 | semidirect |
| 14. #17986379 | C22 | semidirect |
| 17. #17986376 | C22 | semidirect |
| 18. #17986372 | C22 | semidirect |
| 20. #17986350 | C22 | semidirect |
| 25. #17986346 | C22 | semidirect |
| 26. #17986346 | C22 | semidirect |
| 36. #322×C71 | C22 | semidirect |
| 37. #322×C71 | C22 | semidirect |
| 38. C82×C71 | C22 | semidirect |
| 178. #1453 | D71 | semidirect |
| 179. C71 | #19729 | semidirect |
| 206. #322 | C2×D71 | semidirect |
| 207. #322 | C2×D71 | semidirect |
| 208. C82 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599298 | 2 |
| #22599260 | 2 |
| #22599078 | 2 |
| #22598715 | 2 |
| #22588006 | 2 |
| #22588000 | 2 |
| #22587979 | 2 |
| #22587946 | 2 |
| C71×#1453 | 2 |
| #19729 | 71 |