Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
578 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 176 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 |
|---|---|---|
| 21. #17988990 | C4 | semidirect |
| 22. #17988987 | C4 | semidirect |
| 23. #17988985 | C4 | semidirect |
| 26. #498×C73 | C4 | semidirect |
| 128. C73 | #22258 | semidirect |
| 133. #498 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626724 | 2 |
| #22626119 | 2 |
| #22625998 | 2 |
| #22625997 | 2 |
| #22625856 | 2 |
| #22625649 | 2 |
| #22620440 | 2 |
| #22258 | 73 |