Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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. #22612212 | C2 | semidirect |
| 3. #22608138 | C2 | semidirect |
| 4. #22608128 | C2 | semidirect |
| 7. C73×#1426 | C2 | semidirect |
| 22. Dic584 | Q8 | semidirect |
| 24. D1168 | Q8 | semidirect |
| 81. #1426 | D73 | semidirect |
| 85. C73 | #13710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612212 | 2 |
| #22611811 | 2 |
| #22608138 | 2 |
| #22608128 | 2 |
| #22608119 | 2 |
| #22608117 | 2 |
| C73×#1426 | 2 |
| #13710 | 73 |