Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
654 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 654 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×#17989631 | C2 | semidirect |
| 2. #22626334 | C2 | direct (N × H) |
| 3. C2×#17989516 | C2 | semidirect |
| 4. C2×#17989502 | C2 | semidirect |
| 5. C2×#17989474 | C2 | semidirect |
| 10. #17989631 | C22 | semidirect |
| 14. #17989516 | C22 | semidirect |
| 15. #17989502 | C22 | semidirect |
| 16. #17989474 | C22 | semidirect |
| 18. #17989020 | C4 | semidirect |
| 20. C2×#14556534 | C4 | semidirect |
| 21. C2×D1168 | C4 | semidirect |
| 23. C2×Q32×C73 | C4 | semidirect |
| 47. #14556534 | C2×C4 | semidirect |
| 48. D1168 | C2×C4 | semidirect |
| 53. Q32×C73 | C2×C4 | semidirect |
| 128. C2×C73 | #2179 | semidirect |
| 139. C73 | C2×#2179 | semidirect |
| 144. C2×Q32 | #64408 | semidirect |
| 173. Q32 | C2×#64408 | semidirect |
| 263. C2 | #22626334 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989631 | 2 |
| #22626334 | 2 |
| C2×#17989516 | 2 |
| C2×#17989502 | 2 |
| C2×#17989474 | 2 |
| C2×#17989020 | 2 |
| C2×#2179 | 73 |