Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
906 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 906 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. #22598918 | C2 | semidirect |
| 2. #22598917 | C2 | semidirect |
| 3. #22598767 | C2 | semidirect |
| 4. #22598763 | C2 | semidirect |
| 5. #22588013 | C2 | semidirect |
| 6. #22588011 | C2 | semidirect |
| 7. #22588009 | C2 | semidirect |
| 8. #22588007 | C2 | semidirect |
| 9. #22588005 | C2 | semidirect |
| 10. #322×D71 | C2 | semidirect |
| 11. C71×#1721 | C2 | semidirect |
| 113. C8×D71 | D8 | semidirect |
| 202. #1721 | D71 | semidirect |
| 204. C71 | #19616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598918 | 2 |
| #22598917 | 2 |
| #22598767 | 2 |
| #22598763 | 2 |
| #22588013 | 2 |
| #22588011 | 2 |
| #22588009 | 2 |
| #22588007 | 2 |
| #22588005 | 2 |
| #322×D71 | 2 |
| C71×#1721 | 2 |
| #19616 | 71 |