Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
388 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 25. #17988404 | C4 | semidirect |
| 26. #17988403 | C4 | semidirect |
| 27. #17988402 | C4 | semidirect |
| 28. #362×C73 | C4 | semidirect |
| 174. C73 | #12941 | semidirect |
| 193. #362 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626692 | 2 |
| #22626283 | 2 |
| C2×#17989500 | 2 |
| #22626049 | 2 |
| #22624994 | 2 |
| #22624987 | 2 |
| #362×D73 | 2 |
| #12941 | 73 |