Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
492 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #22610875 | C2 | semidirect |
| 5. #22608481 | C2 | semidirect |
| 6. #22607786 | C2 | semidirect |
| 7. C73×#1288 | C2 | semidirect |
| 10. #17988981 | C4 | semidirect |
| 11. #17988947 | C4 | semidirect |
| 36. #14556591 | C2×C4 | semidirect |
| 37. #14556591 | C2×C4 | semidirect |
| 71. #97×C73 | C2×C4 | semidirect |
| 210. #1288 | D73 | semidirect |
| 212. C73 | #9379 | semidirect |
| 273. #97 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620936 | 2 |
| #22612741 | 2 |
| #22610875 | 2 |
| #22608528 | 2 |
| #22608481 | 2 |
| #22607786 | 2 |
| C73×#1288 | 2 |
| #9379 | 73 |