Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
418 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 76 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. #22626110 | C2 | semidirect |
| 3. #22625465 | C2 | semidirect |
| 5. #22624795 | C2 | semidirect |
| 6. #22624781 | C2 | semidirect |
| 26. #17988997 | C4 | semidirect |
| 27. #17988949 | C4 | semidirect |
| 28. #17988947 | C4 | semidirect |
| 34. #501×C73 | C4 | semidirect |
| 212. C73 | #9375 | semidirect |
| 216. #501 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626871 | 2 |
| #22626110 | 2 |
| #22625465 | 2 |
| #22625334 | 2 |
| #22624795 | 2 |
| #22624781 | 2 |
| #22621153 | 2 |
| #9375 | 73 |