Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #22611704 | C2 | semidirect |
| 3. C2×#17988403 | C2 | semidirect |
| 6. #22608032 | C2 | semidirect |
| 7. C73×#2141 | C2 | semidirect |
| 163. #2141 | D73 | semidirect |
| 167. C73 | #13397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619582 | 2 |
| #22611704 | 2 |
| C2×#17988403 | 2 |
| #22611558 | 2 |
| #22609982 | 2 |
| #22608032 | 2 |
| C73×#2141 | 2 |
| #13397 | 73 |