Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1602 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1602 conjugacy classes of subgroups — too many to draw. Only its 275 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. #22610008 | C2 | semidirect |
| 4. #22610006 | C2 | semidirect |
| 5. #22610004 | C2 | semidirect |
| 6. #342×D73 | C2 | semidirect |
| 7. C73×#1820 | C2 | semidirect |
| 10. C2×C4×D292 | C4 | semidirect |
| 11. C2×#14556553 | C4 | semidirect |
| 32. C22×C4×D73 | C2×C4 | semidirect |
| 36. C2×C4⋊Dic73 | C2×C4 | semidirect |
| 42. C2×#11924005 | C2×C4 | semidirect |
| 46. C2×C4×Dic73 | C2×C4 | semidirect |
| 50. C2×C4⋊C4×C73 | C2×C4 | semidirect |
| 53. C2×C42×C73 | C2×C4 | semidirect |
| 163. #1820 | D73 | semidirect |
| 166. C73 | #20689 | semidirect |
| 198. C2×C4⋊C4 | C4×D73 | semidirect |
| 211. C2×C42 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989061 | 2 |
| #22612508 | 2 |
| #22610008 | 2 |
| #22610006 | 2 |
| #22610004 | 2 |
| #342×D73 | 2 |
| C73×#1820 | 2 |
| #20689 | 73 |