Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
648 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#17988455 | C2 | semidirect |
| 4. #22607811 | C2 | semidirect |
| 5. C73×#1817 | C2 | semidirect |
| 8. #17988489 | C4 | semidirect |
| 9. #17988485 | C4 | semidirect |
| 169. #1817 | D73 | semidirect |
| 172. C73 | #9157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618262 | 2 |
| C2×#17988455 | 2 |
| C2×#17988322 | 2 |
| #22607811 | 2 |
| C73×#1817 | 2 |
| #9157 | 73 |