Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22611703 | C2 | semidirect |
| 3. #22611660 | C2 | semidirect |
| 4. #22611535 | C2 | semidirect |
| 5. #22610842 | C2 | semidirect |
| 6. #22610827 | C2 | semidirect |
| 7. C73×#2140 | C2 | semidirect |
| 11. C2×#14556535 | C4 | semidirect |
| 12. C2×#14556532 | C4 | semidirect |
| 171. #2140 | D73 | semidirect |
| 175. C73 | #13247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989023 | 2 |
| #22611703 | 2 |
| #22611660 | 2 |
| #22611535 | 2 |
| #22610842 | 2 |
| #22610827 | 2 |
| C73×#2140 | 2 |
| #13247 | 73 |