Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
350 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 74 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×#17989478 | C2 | semidirect |
| 4. #22626040 | C2 | semidirect |
| 5. #22625002 | C2 | semidirect |
| 6. #22624996 | C2 | semidirect |
| 21. #17988389 | C4 | semidirect |
| 22. #17988388 | C4 | semidirect |
| 23. #17988387 | C4 | semidirect |
| 24. #357×C73 | C4 | semidirect |
| 175. C73 | #13155 | semidirect |
| 190. #357 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989505 | 2 |
| C2×#17989478 | 2 |
| #22626080 | 2 |
| #22626040 | 2 |
| #22625002 | 2 |
| #22624996 | 2 |
| #22611645 | 2 |
| #13155 | 73 |