Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
786 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. #22613571 | C2 | semidirect |
| 5. #22608502 | C2 | semidirect |
| 6. #22607778 | C2 | semidirect |
| 7. C73×#1787 | C2 | semidirect |
| 109. C22⋊Dic73 | SD16 | semidirect |
| 236. #1787 | D73 | semidirect |
| 239. C73 | #9949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620689 | 2 |
| C2×#17988726 | 2 |
| #22613571 | 2 |
| #22610766 | 2 |
| #22608502 | 2 |
| #22607778 | 2 |
| C73×#1787 | 2 |
| #9949 | 73 |