Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 11. #17989428 | C4 | semidirect |
| 12. C8×#10596833 | C4 | semidirect |
| 15. #17988309 | C4 | semidirect |
| 16. C8×#10596831 | C4 | semidirect |
| 17. C82×C73 | C4 | semidirect |
| 23. #14556645 | C8 | semidirect |
| 94. C73 | #8138 | semidirect |
| 106. C82 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625587 | 2 |
| #22625135 | 2 |
| #22624756 | 2 |
| #22624754 | 2 |
| #22608213 | 2 |
| #8138 | 73 |