Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
454 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 12. C8×#10596831 | C4 | semidirect |
| 13. C8×#10596831 | C4 | semidirect |
| 14. C8×#10596831 | C4 | semidirect |
| 15. C82×C73 | C4 | semidirect |
| 70. C8×C73 | #106 | semidirect |
| 71. C8×C73 | #107 | semidirect |
| 73. #10596831 | #106 | semidirect |
| 74. #10596831 | #107 | semidirect |
| 97. C73 | #8814 | semidirect |
| 108. C82 | #64408 | semidirect |
| 166. C8 | #14556659 | semidirect |
| 167. C8 | #14556660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625867 | 2 |
| #22625866 | 2 |
| #22625852 | 2 |
| C82×D73 | 2 |
| #8814 | 73 |