Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
464 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22610136 | C2 | semidirect |
| 3. #22610114 | C2 | semidirect |
| 5. #22607817 | C2 | semidirect |
| 6. #22607779 | C2 | semidirect |
| 22. #17988324 | C4 | semidirect |
| 23. #17988324 | C4 | semidirect |
| 24. #17988321 | C4 | semidirect |
| 25. #17988321 | C4 | semidirect |
| 225. C73 | #8874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618979 | 2 |
| #22610136 | 2 |
| #22610114 | 2 |
| #22608422 | 2 |
| #22607817 | 2 |
| #22607779 | 2 |
| C73×#1871 | 2 |
| #8874 | 73 |