Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
254 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 27. C2×Dic292 | C8 | semidirect |
| 32. C2×Q16×C73 | C8 | semidirect |
| 124. C73 | #7113 | semidirect |
| 137. C2×Q16 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627002 | 2 |
| #22626937 | 2 |
| #22626077 | 2 |
| #7113 | 73 |