Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
544 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 10. C2×C4×Dic146 | C4 | semidirect |
| 12. #17988493 | C4 | semidirect |
| 15. #17988453 | C4 | semidirect |
| 17. C43×C73 | C4 | semidirect |
| 55. C2×Dic146 | C4⋊C4 | semidirect |
| 87. C42×C73 | C4⋊C4 | semidirect |
| 146. C4×C73 | #354 | semidirect |
| 162. C73 | #12798 | semidirect |
| 173. C43 | #64408 | semidirect |
| 245. C42 | C4⋊#64408 | semidirect |
| 307. C4 | #17989494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989494 | 2 |
| #22625792 | 2 |
| #22625025 | 2 |
| C4×#14556579 | 2 |
| #12798 | 73 |