Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
190 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 80 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. #22625097 | C2 | direct (N × H) |
| 12. #17988420 | C4 | semidirect |
| 14. C2×#14556497 | C4 | semidirect |
| 15. C2×C32×C73 | C4 | semidirect |
| 28. #14556497 | C2×C4 | semidirect |
| 30. C32×C73 | C2×C4 | semidirect |
| 72. C2×C73 | #1426 | semidirect |
| 80. C73 | C2×#1426 | semidirect |
| 87. C2×C32 | #64408 | semidirect |
| 106. C32 | C2×#64408 | semidirect |
| 149. C2 | #22625097 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989516 | 2 |
| C2×#17989514 | 2 |
| #22625097 | 2 |
| C2×#17988420 | 2 |
| C2×#1426 | 73 |