Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
490 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 22. C2×Dic584 | C4 | semidirect |
| 23. C2×#14556537 | C4 | semidirect |
| 24. C2×#14556537 | C4 | semidirect |
| 28. C2×Q32×C73 | C4 | semidirect |
| 140. C2×#64408 | Q32 | semidirect |
| 206. C73 | #13015 | semidirect |
| 215. C2×Q32 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×#64408 | 2 |
| C2×#17989500 | 2 |
| #22626077 | 2 |
| #22624989 | 2 |
| #22624968 | 2 |
| C2×Q32×D73 | 2 |
| #13015 | 73 |