Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
892 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 892 conjugacy classes of subgroups — too many to draw. Only its 122 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. #22625822 | C2 | semidirect |
| 2. #22625594 | C2 | semidirect |
| 3. #22624747 | C2 | semidirect |
| 9. #17989453 | C22 | semidirect |
| 10. #17989453 | C22 | semidirect |
| 100. C2×D4×C73 | M16 | semidirect |
| 204. C73 | #7606 | semidirect |
| 267. C2×D4 | #11924037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625822 | 2 |
| #22625594 | 2 |
| #22624747 | 2 |
| C2×#17988490 | 2 |
| #7606 | 73 |