Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 90 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. #22626900 | C2 | semidirect |
| 2. #22626253 | C2 | semidirect |
| 3. #22625814 | C2 | semidirect |
| 4. #22625004 | C2 | semidirect |
| 17. #17988842 | C4 | semidirect |
| 18. #17988841 | C4 | semidirect |
| 19. #17988840 | C4 | semidirect |
| 24. #470×C73 | C4 | semidirect |
| 27. #14556666 | D4 | semidirect |
| 183. C73 | #13077 | semidirect |
| 192. #470 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626900 | 2 |
| #22626253 | 2 |
| #22625814 | 2 |
| #22625004 | 2 |
| #22619595 | 2 |
| #13077 | 73 |