Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 2. #22611717 | C2 | semidirect |
| 4. #22608038 | C2 | semidirect |
| 14. #17988369 | C4 | semidirect |
| 29. #14556531 | C2×C4 | semidirect |
| 149. C73 | #12923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618521 | 2 |
| #22611717 | 2 |
| C2×#17988369 | 2 |
| #22608038 | 2 |
| C73×#1809 | 2 |
| #12923 | 73 |