Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
486 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #22608686 | C2 | semidirect |
| 4. #22607805 | C2 | semidirect |
| 106. #10596831 | #100 | semidirect |
| 136. C73 | #8614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#10596831 | 2 |
| #22609923 | 2 |
| #22608686 | 2 |
| #22607805 | 2 |
| C73×#1800 | 2 |
| #8614 | 73 |