Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
330 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 172 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. #22624842 | C2 | semidirect |
| 4. C16×#10596833 | C2 | semidirect |
| 19. #14556666 | C8 | semidirect |
| 29. C16×D73 | C8 | semidirect |
| 30. C16×D73 | C8 | semidirect |
| 86. C73 | #11399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626138 | 2 |
| #22625135 | 2 |
| #22624842 | 2 |
| C16×#10596833 | 2 |
| C4×C16×D73 | 2 |
| #11399 | 73 |