Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
522 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 104 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. #22625667 | C2 | semidirect |
| 2. C8×C22⋊#64408 | C2 | semidirect |
| 5. #22624813 | C2 | semidirect |
| 6. #22624811 | C2 | semidirect |
| 16. #17989441 | C4 | semidirect |
| 17. #17989441 | C4 | semidirect |
| 18. #17989438 | C4 | semidirect |
| 19. #17989438 | C4 | semidirect |
| 20. C2×#14556598 | C4 | semidirect |
| 27. #17988613 | C4 | semidirect |
| 29. #17988545 | C4 | semidirect |
| 30. #408×C73 | C4 | semidirect |
| 216. C73 | #8240 | semidirect |
| 225. #408 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625667 | 2 |
| C8×C22⋊#64408 | 2 |
| #22625306 | 2 |
| #22624813 | 2 |
| #22624811 | 2 |
| #22618628 | 2 |
| #8240 | 73 |