Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
248 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 102 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. #22624850 | C2 | semidirect |
| 4. #22624850 | C2 | semidirect |
| 5. #22624848 | C2 | semidirect |
| 6. #22624847 | C2 | semidirect |
| 65. #11924003 | M16 | semidirect |
| 72. C16×C73 | M16 | semidirect |
| 116. C73 | #11414 | semidirect |
| 181. C16 | #11924037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626293 | 2 |
| #22625140 | 2 |
| #22624850 | 2 |
| #22624848 | 2 |
| #22624847 | 2 |
| M32×Dic73 | 2 |
| #11414 | 73 |