Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 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 |
|---|---|---|
| 4. #22608483 | C2 | semidirect |
| 5. #22608481 | C2 | semidirect |
| 6. #22607796 | C2 | semidirect |
| 7. C73×#1288 | C2 | semidirect |
| 11. #17988934 | C4 | semidirect |
| 12. #17988934 | C4 | semidirect |
| 29. #14556591 | C2×C4 | semidirect |
| 30. #14556591 | C2×C4 | semidirect |
| 58. C4×C8×C73 | C2×C4 | semidirect |
| 174. #1288 | D73 | semidirect |
| 175. C73 | #9425 | semidirect |
| 223. C4×C8 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620306 | 2 |
| #22613107 | 2 |
| #22608644 | 2 |
| #22608483 | 2 |
| #22608481 | 2 |
| #22607796 | 2 |
| C73×#1288 | 2 |
| #9425 | 73 |