Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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. #22610651 | C2 | semidirect |
| 4. #22610492 | C2 | semidirect |
| 6. #22610076 | C2 | semidirect |
| 7. C73×#1843 | C2 | semidirect |
| 121. #1843 | D73 | semidirect |
| 123. C73 | #23380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22613229 | 2 |
| #22610651 | 2 |
| #22610543 | 2 |
| #22610492 | 2 |
| #22610107 | 2 |
| #22610076 | 2 |
| C73×#1843 | 2 |
| #23380 | 73 |