Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
380 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22608659 | C2 | semidirect |
| 5. #22608525 | C2 | semidirect |
| 6. #22607802 | C2 | semidirect |
| 7. C73×#1569 | C2 | semidirect |
| 183. #1569 | D73 | semidirect |
| 188. C73 | #10498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620936 | 2 |
| #22610778 | 2 |
| #22608659 | 2 |
| #22608528 | 2 |
| #22608525 | 2 |
| #22607802 | 2 |
| C73×#1569 | 2 |
| #10498 | 73 |