Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
374 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 5. C2×#14556527 | C4 | semidirect |
| 13. C22⋊C16×C73 | C4 | semidirect |
| 122. C73 | #7264 | semidirect |
| 129. C22⋊C16 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22609969 | 2 |
| C2×#17988350 | 2 |
| C73×#2112 | 2 |
| #7264 | 73 |