Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22590657 | C2 | semidirect |
| 2. C2×#17985837 | C2 | semidirect |
| 3. #22590465 | C2 | semidirect |
| 4. #22586530 | C2 | semidirect |
| 5. #22586524 | C2 | semidirect |
| 6. #22586482 | C2 | semidirect |
| 8. C2×Dic568 | C22 | semidirect |
| 13. #17985833 | C22 | semidirect |
| 14. C2×C71⋊C32 | C22 | semidirect |
| 15. #17985829 | C22 | semidirect |
| 127. C71 | #13671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590657 | 2 |
| C2×#17985837 | 2 |
| #22590465 | 2 |
| #22586530 | 2 |
| #22586524 | 2 |
| #22586482 | 2 |
| C71×#3415 | 2 |
| #13671 | 71 |