Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
342 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 1. C2×#17989518 | C2 | semidirect |
| 2. #22625045 | C2 | semidirect |
| 3. C22⋊#14556641 | C2 | semidirect |
| 6. C2×#14556641 | C22 | semidirect |
| 64. C22×D73 | C32 | semidirect |
| 87. C22×C73 | C2×C32 | semidirect |
| 94. C2×D73 | C2×C32 | semidirect |
| 107. D73 | C22⋊C32 | semidirect |
| 112. C73 | C2×C22⋊C32 | semidirect |
| 202. C22 | #17989518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989518 | 2 |
| #22625045 | 2 |
| C22⋊#14556641 | 2 |
| C22×C16×D73 | 2 |
| C2×C22⋊C32 | 73 |