Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1068 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22609874 | C2 | semidirect |
| 3. C4×#14556506 | C2 | semidirect |
| 4. #22608452 | C2 | semidirect |
| 5. C73×#1465 | C2 | semidirect |
| 7. C23×Dic146 | C4 | semidirect |
| 10. C2×#14556579 | C4 | semidirect |
| 14. C2×#14556565 | C4 | semidirect |
| 16. C2×C4×Dic146 | C4 | semidirect |
| 152. C23×C73 | #104 | semidirect |
| 198. Dic146 | #99 | semidirect |
| 243. #1465 | D73 | semidirect |
| 244. C73 | #8366 | semidirect |
| 396. C23 | #14556517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989246 | 2 |
| #22609874 | 2 |
| C4×#14556506 | 2 |
| #22608452 | 2 |
| C73×#1465 | 2 |
| #8366 | 73 |