Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
620 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 1. #22626475 | C2 | semidirect |
| 2. #22625459 | C2 | semidirect |
| 3. #22625351 | C2 | semidirect |
| 4. #22624791 | C2 | semidirect |
| 16. #17988963 | C4 | semidirect |
| 17. #17988960 | C4 | semidirect |
| 18. #17988959 | C4 | semidirect |
| 20. #493×C73 | C4 | semidirect |
| 39. #14556591 | C2×C4 | semidirect |
| 48. C4×#10596831 | C2×C4 | semidirect |
| 51. #127×C73 | C2×C4 | semidirect |
| 52. C4×C8×C73 | C2×C4 | semidirect |
| 154. C73 | #9428 | semidirect |
| 160. #493 | #64408 | semidirect |
| 186. #127 | C2×#64408 | semidirect |
| 198. C4×C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626475 | 2 |
| #22625459 | 2 |
| #22625351 | 2 |
| #22624791 | 2 |
| #22620382 | 2 |
| #9428 | 73 |