Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
394 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 394 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 |
| 4. #22611535 | C2 | semidirect |
| 5. #22610847 | C2 | semidirect |
| 7. C73×#2141 | C2 | semidirect |
| 11. C2×#14556537 | C4 | semidirect |
| 12. C2×#14556534 | C4 | semidirect |
| 166. #2141 | D73 | semidirect |
| 170. C73 | #13248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989028 | 2 |
| #22611703 | 2 |
| #22611660 | 2 |
| #22611535 | 2 |
| #22610847 | 2 |
| #22610827 | 2 |
| C73×#2141 | 2 |
| #13248 | 73 |