Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22627094 | C2 | semidirect |
| 4. #22627010 | C2 | semidirect |
| 10. C2×#14556687 | C4 | semidirect |
| 12. C22×#11924040 | C4 | semidirect |
| 13. #17989685 | C4 | semidirect |
| 115. C73 | #12613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989708 | 2 |
| #22627108 | 2 |
| #22627094 | 2 |
| #22627010 | 2 |
| #22625688 | 2 |
| #12613 | 73 |