Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
380 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 1. #22627125 | C2 | semidirect |
| 2. #22627040 | C2 | semidirect |
| 3. #22626981 | C2 | semidirect |
| 7. #17989692 | C22 | semidirect |
| 10. C8×#10596842 | C22 | semidirect |
| 46. #14556610 | C8 | semidirect |
| 48. C2×Dic292 | C8 | semidirect |
| 51. C2×D8×C73 | C8 | semidirect |
| 145. C73 | #11602 | semidirect |
| 168. C2×D8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627125 | 2 |
| #22627040 | 2 |
| #22626981 | 2 |
| C2×#17989629 | 2 |
| #11602 | 73 |