Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
212 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 42. Q16×C73 | C16 | semidirect |
| 74. C73 | #12059 | semidirect |
| 99. Q16 | #11924040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924040 | 2 |
| #22626989 | 2 |
| Q8⋊#11924040 | 2 |
| #22626948 | 2 |
| Q16×#10596833 | 2 |
| #12059 | 73 |