Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
382 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 110 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. #22626151 | C2 | semidirect |
| 4. #22624987 | C2 | semidirect |
| 8. C2×#14556666 | C4 | semidirect |
| 10. C2×#14556665 | C4 | semidirect |
| 11. C2×#14556664 | C4 | semidirect |
| 13. C22×#11924031 | C4 | semidirect |
| 22. #17988369 | C4 | semidirect |
| 23. #17988368 | C4 | semidirect |
| 24. #349×C73 | C4 | semidirect |
| 142. C73 | #12617 | semidirect |
| 158. #349 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989646 | 2 |
| #22626151 | 2 |
| #22625687 | 2 |
| #22624987 | 2 |
| #22611550 | 2 |
| #12617 | 73 |