Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
462 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 2. C2×Q32×D73 | C2 | semidirect |
| 3. #22612250 | C2 | direct (N × H) |
| 4. C2×#17988427 | C2 | semidirect |
| 5. C2×#17988426 | C2 | semidirect |
| 6. C2×#17988424 | C2 | semidirect |
| 7. C2×#17988420 | C2 | semidirect |
| 8. C2×Q64×C73 | C2 | semidirect |
| 16. Q32×D73 | C22 | semidirect |
| 20. #17988427 | C22 | semidirect |
| 21. #17988426 | C22 | semidirect |
| 22. #17988424 | C22 | semidirect |
| 23. #17988420 | C22 | semidirect |
| 27. Q64×C73 | C22 | semidirect |
| 124. C2×C73 | #2264 | semidirect |
| 132. C2×Q64 | D73 | semidirect |
| 136. C73 | C2×#2264 | semidirect |
| 151. Q64 | C2×D73 | semidirect |
| 253. C2 | #22612250 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989020 | 2 |
| C2×Q32×D73 | 2 |
| #22612250 | 2 |
| C2×#17988427 | 2 |
| C2×#17988426 | 2 |
| C2×#17988424 | 2 |
| C2×#17988420 | 2 |
| C2×Q64×C73 | 2 |
| C2×#2264 | 73 |