Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 120 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. #22626898 | C2 | semidirect |
| 2. #22626167 | C2 | semidirect |
| 3. C2×#17989483 | C2 | semidirect |
| 4. #22624981 | C2 | semidirect |
| 25. #14556665 | D4 | semidirect |
| 146. C73 | #12989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626898 | 2 |
| #22626167 | 2 |
| C2×#17989483 | 2 |
| #22624981 | 2 |
| #22618635 | 2 |
| #12989 | 73 |