Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
284 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22612251 | C2 | semidirect |
| 3. C2×#17988426 | C2 | semidirect |
| 4. #22612056 | C2 | semidirect |
| 5. #22608122 | C2 | semidirect |
| 6. #22608116 | C2 | semidirect |
| 7. C73×#1401 | C2 | semidirect |
| 13. C2×Dic584 | C22 | semidirect |
| 20. #17988417 | C22 | semidirect |
| 23. M64×C73 | C22 | semidirect |
| 24. C2×C32×C73 | C22 | semidirect |
| 126. #1401 | D73 | semidirect |
| 127. C73 | #13671 | semidirect |
| 141. M64 | C2×D73 | semidirect |
| 142. C2×C32 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623072 | 2 |
| #22612251 | 2 |
| C2×#17988426 | 2 |
| #22612056 | 2 |
| #22608122 | 2 |
| #22608116 | 2 |
| C73×#1401 | 2 |
| #13671 | 73 |