Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
622 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22614836 | C2 | semidirect |
| 3. #22608491 | C2 | semidirect |
| 4. #22608355 | C2 | semidirect |
| 5. #22608326 | C2 | semidirect |
| 6. #22607791 | C2 | semidirect |
| 7. C73×#3037 | C2 | semidirect |
| 120. C2×Q8×C73 | D8 | semidirect |
| 245. #3037 | D73 | semidirect |
| 251. C73 | #9997 | semidirect |
| 341. C2×Q8 | #11924013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619927 | 2 |
| #22614836 | 2 |
| #22608491 | 2 |
| #22608355 | 2 |
| #22608326 | 2 |
| #22607791 | 2 |
| C73×#3037 | 2 |
| #9997 | 73 |