Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
366 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. #22625011 | C2 | semidirect |
| 4. #22624994 | C2 | semidirect |
| 15. #17988636 | C4 | semidirect |
| 17. #17988634 | C4 | semidirect |
| 21. #430×C73 | C4 | semidirect |
| 138. C73 | #12877 | semidirect |
| 146. #430 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626162 | 2 |
| #22625814 | 2 |
| #22625011 | 2 |
| #22624994 | 2 |
| #22618541 | 2 |
| #12877 | 73 |