Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
668 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 106 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. C4×#14556648 | C2 | semidirect |
| 2. C2×#17989441 | C2 | semidirect |
| 4. #22625107 | C2 | semidirect |
| 14. C2×#14556580 | C4 | semidirect |
| 18. #17988489 | C4 | semidirect |
| 23. #17988452 | C4 | semidirect |
| 24. #391×C73 | C4 | semidirect |
| 227. C73 | #9681 | semidirect |
| 234. #391 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556648 | 2 |
| C2×#17989441 | 2 |
| C2×#17989439 | 2 |
| #22625107 | 2 |
| #22618235 | 2 |
| #9681 | 73 |