Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
378 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 100 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. #22625484 | C2 | semidirect |
| 4. M16×#10596833 | C2 | semidirect |
| 5. #22624777 | C2 | semidirect |
| 6. #22624764 | C2 | semidirect |
| 51. #14556508 | C8 | semidirect |
| 175. C73 | #9550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625484 | 2 |
| #22625230 | 2 |
| C2×D4⋊#10596833 | 2 |
| M16×#10596833 | 2 |
| #22624777 | 2 |
| #22624764 | 2 |
| #100×Dic73 | 2 |
| #9550 | 73 |