Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
386 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 86 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×#17989474 | C2 | semidirect |
| 4. #22626035 | C2 | semidirect |
| 5. #22624989 | C2 | semidirect |
| 6. #22624988 | C2 | semidirect |
| 21. #17988389 | C4 | semidirect |
| 22. #17988388 | C4 | semidirect |
| 23. #17988387 | C4 | semidirect |
| 24. #357×C73 | C4 | semidirect |
| 190. C73 | #13149 | semidirect |
| 205. #357 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989499 | 2 |
| C2×#17989474 | 2 |
| #22626078 | 2 |
| #22626035 | 2 |
| #22624989 | 2 |
| #22624988 | 2 |
| #357×D73 | 2 |
| #13149 | 73 |