Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
520 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 74 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. #22626473 | C2 | semidirect |
| 4. #22625329 | C2 | semidirect |
| 5. #22624833 | C2 | semidirect |
| 6. #22624780 | C2 | semidirect |
| 26. #17988923 | C4 | semidirect |
| 27. #17988920 | C4 | semidirect |
| 31. #17988738 | C4 | semidirect |
| 34. #450×C73 | C4 | semidirect |
| 262. C73 | #9344 | semidirect |
| 271. #450 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626473 | 2 |
| #22626070 | 2 |
| #22625336 | 2 |
| #22625329 | 2 |
| #22624833 | 2 |
| #22624780 | 2 |
| #22620734 | 2 |
| #9344 | 73 |