Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
490 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 221 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. #22627158 | C2 | semidirect |
| 2. #22627156 | C2 | semidirect |
| 27. #14556686 | Q8 | semidirect |
| 111. C73 | #33475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627158 | 2 |
| #22627156 | 2 |
| #22627123 | 2 |
| #22627120 | 2 |
| #22627093 | 2 |
| #22627087 | 2 |
| #22626721 | 2 |
| #33475 | 73 |