Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1708 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1708 conjugacy classes of subgroups — too many to draw. Only its 288 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. C24×#10596833 | C2 | semidirect |
| 2. C2×#17989616 | C2 | semidirect |
| 3. #22625906 | C2 | semidirect |
| 4. #22625874 | C2 | semidirect |
| 5. #22625753 | C2 | semidirect |
| 6. #22625668 | C2 | semidirect |
| 8. C22×#11924038 | C22 | semidirect |
| 13. C2×C4⋊#10596833 | C22 | semidirect |
| 14. C2×#14556648 | C22 | semidirect |
| 17. C2×#14556646 | C22 | semidirect |
| 18. #17989453 | C22 | semidirect |
| 31. C22×#10596833 | D4 | semidirect |
| 91. C24×C73 | M16 | semidirect |
| 129. #10596833 | #120 | semidirect |
| 135. C22×C73 | #435 | semidirect |
| 161. C73 | #21440 | semidirect |
| 215. C24 | #11924038 | semidirect |
| 292. C22 | #17989616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#10596833 | 2 |
| C2×#17989616 | 2 |
| #22625906 | 2 |
| #22625874 | 2 |
| #22625753 | 2 |
| #22625668 | 2 |
| #22612430 | 2 |
| #21440 | 73 |