Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
454 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 100 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. #22625484 | C2 | semidirect |
| 4. #22625482 | C2 | semidirect |
| 5. #22624764 | C2 | semidirect |
| 6. #22624764 | C2 | semidirect |
| 88. #11924012 | M16 | semidirect |
| 110. M16×C73 | M16 | semidirect |
| 185. C73 | #8837 | semidirect |
| 269. M16 | #11924037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626793 | 2 |
| #22626052 | 2 |
| #22625484 | 2 |
| #22625482 | 2 |
| #22624764 | 2 |
| #100×Dic73 | 2 |
| #8837 | 73 |