Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1318 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 195 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. C2×#17986611 | C2 | semidirect |
| 3. #22589486 | C2 | semidirect |
| 4. #22589422 | C2 | semidirect |
| 5. #22588698 | C2 | semidirect |
| 6. #22588652 | C2 | semidirect |
| 7. #22588411 | C2 | semidirect |
| 11. C2×#14556128 | C22 | semidirect |
| 13. C2×#14556120 | C22 | semidirect |
| 16. C2×C4×Dic142 | C22 | semidirect |
| 18. C2×#14556051 | C22 | semidirect |
| 21. #17985761 | C22 | semidirect |
| 22. #17985754 | C22 | semidirect |
| 23. #17985754 | C22 | semidirect |
| 195. C71 | #23942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986611 | 2 |
| C2×#17986150 | 2 |
| #22589486 | 2 |
| #22589422 | 2 |
| #22588698 | 2 |
| #22588652 | 2 |
| #22588411 | 2 |
| C71×#2309 | 2 |
| #23942 | 71 |