Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
886 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 886 conjugacy classes of subgroups — too many to draw. Only its 159 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. #22611680 | C2 | semidirect |
| 2. C2×#17988394 | C2 | semidirect |
| 3. #22611545 | C2 | semidirect |
| 4. #22609981 | C2 | semidirect |
| 6. C2×#14556531 | C22 | semidirect |
| 7. C22×#11924003 | C22 | semidirect |
| 8. C2×#14556527 | C22 | semidirect |
| 173. C73 | #12746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611680 | 2 |
| C2×#17988394 | 2 |
| #22611545 | 2 |
| #22609981 | 2 |
| C73×#3584 | 2 |
| #12746 | 73 |