Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1026 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 255 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. #22610730 | C2 | semidirect |
| 2. #22610546 | C2 | semidirect |
| 3. #22610229 | C2 | semidirect |
| 4. #22609841 | C2 | semidirect |
| 6. C22×#11924012 | C22 | semidirect |
| 7. C2×C4⋊#10596831 | C22 | semidirect |
| 10. C2×C22⋊#10596831 | C22 | semidirect |
| 11. C2×#14556502 | C22 | semidirect |
| 12. #17988342 | C22 | semidirect |
| 52. C24×C73 | M16 | semidirect |
| 140. C73 | #23309 | semidirect |
| 182. C24 | #11924012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610730 | 2 |
| #22610546 | 2 |
| #22610229 | 2 |
| #22609841 | 2 |
| C4×#120×C73 | 2 |
| #23309 | 73 |