Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
508 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. #22626789 | C2 | semidirect |
| 2. #22625701 | C2 | semidirect |
| 3. #22625401 | C2 | semidirect |
| 4. #22625311 | C2 | semidirect |
| 5. #22624824 | C2 | semidirect |
| 6. #22624783 | C2 | semidirect |
| 25. #17988878 | C4 | semidirect |
| 26. #17988877 | C4 | semidirect |
| 27. #17988779 | C4 | semidirect |
| 32. #459×C73 | C4 | semidirect |
| 228. C73 | #9163 | semidirect |
| 235. #459 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626789 | 2 |
| #22625701 | 2 |
| #22625401 | 2 |
| #22625311 | 2 |
| #22624824 | 2 |
| #22624783 | 2 |
| #22620021 | 2 |
| #9163 | 73 |