Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
306 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 42. #14556527 | C8 | semidirect |
| 43. #14556526 | C8 | semidirect |
| 44. #108×C73 | C8 | semidirect |
| 122. C73 | #9607 | semidirect |
| 147. #108 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627056 | 2 |
| C2×#17989676 | 2 |
| #22627040 | 2 |
| #22626943 | 2 |
| #108×#64408 | 2 |
| #9607 | 73 |