Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
452 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22601490 | C2 | semidirect |
| 2. #22601489 | C2 | semidirect |
| 3. #22590660 | C2 | semidirect |
| 4. #22590659 | C2 | semidirect |
| 5. #22590656 | C2 | semidirect |
| 6. #22590648 | C2 | semidirect |
| 7. #22590647 | C2 | semidirect |
| 8. C2×#17985839 | C2 | semidirect |
| 9. Q64×D71 | C2 | semidirect |
| 10. #22590635 | C2 | semidirect |
| 11. C71×#2264 | C2 | semidirect |
| 165. #2264 | D71 | semidirect |
| 171. C71 | #33984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601490 | 2 |
| #22601489 | 2 |
| #22590660 | 2 |
| #22590659 | 2 |
| #22590656 | 2 |
| #22590648 | 2 |
| #22590647 | 2 |
| C2×#17985839 | 2 |
| Q64×D71 | 2 |
| #22590635 | 2 |
| C71×#2264 | 2 |
| #33984 | 71 |