Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
662 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 184 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×#17989629 | C2 | semidirect |
| 2. #22626330 | C2 | direct (N × H) |
| 3. C2×#17989515 | C2 | semidirect |
| 4. C2×#17989501 | C2 | semidirect |
| 5. C2×C16×#64408 | C2 | semidirect |
| 10. #17989629 | C22 | semidirect |
| 14. #17989515 | C22 | semidirect |
| 15. #17989501 | C22 | semidirect |
| 16. C16×#64408 | C22 | semidirect |
| 18. #17989016 | C4 | semidirect |
| 20. C2×Dic584 | C4 | semidirect |
| 21. C2×#14556535 | C4 | semidirect |
| 23. C2×D16×C73 | C4 | semidirect |
| 47. Dic584 | C2×C4 | semidirect |
| 48. #14556535 | C2×C4 | semidirect |
| 53. D16×C73 | C2×C4 | semidirect |
| 131. C2×C73 | #2178 | semidirect |
| 141. C73 | C2×#2178 | semidirect |
| 148. C2×D16 | #64408 | semidirect |
| 177. D16 | C2×#64408 | semidirect |
| 267. C2 | #22626330 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989629 | 2 |
| #22626330 | 2 |
| C2×#17989515 | 2 |
| C2×#17989501 | 2 |
| C2×C16×#64408 | 2 |
| C2×#17989016 | 2 |
| C2×#2178 | 73 |