Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1026 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 194 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. #22626055 | C2 | semidirect |
| 2. #22626004 | C2 | semidirect |
| 3. #22625908 | C2 | semidirect |
| 4. #22625753 | C2 | semidirect |
| 6. C22×#11924037 | C22 | semidirect |
| 7. C2×#14556658 | C22 | semidirect |
| 10. C2×C22⋊#10596833 | C22 | semidirect |
| 11. C2×#14556646 | C22 | semidirect |
| 12. #17989453 | C22 | semidirect |
| 72. C24×C73 | M16 | semidirect |
| 140. C73 | #23309 | semidirect |
| 182. C24 | #11924037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626055 | 2 |
| #22626004 | 2 |
| #22625908 | 2 |
| #22625753 | 2 |
| #120×Dic73 | 2 |
| #23309 | 73 |