Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
486 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. C2×#17989681 | C2 | semidirect |
| 4. #22627001 | C2 | semidirect |
| 7. C2×#14556686 | C4 | semidirect |
| 11. #17989684 | C4 | semidirect |
| 43. #11924040 | C22⋊C4 | semidirect |
| 103. C2×D73 | #346 | semidirect |
| 122. C73 | #12611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556686 | 2 |
| C2×#17989684 | 2 |
| C2×#17989681 | 2 |
| #22627001 | 2 |
| #22625665 | 2 |
| #12611 | 73 |