Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 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. C2×#17988399 | C2 | semidirect |
| 3. #22611648 | C2 | semidirect |
| 4. #22611558 | C2 | semidirect |
| 5. #22609986 | C2 | semidirect |
| 6. #22608032 | C2 | semidirect |
| 7. C73×#2155 | C2 | semidirect |
| 57. C2×C16×C73 | D4 | semidirect |
| 167. #2155 | D73 | semidirect |
| 173. C73 | #13396 | semidirect |
| 219. C2×C16 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619580 | 2 |
| C2×#17988399 | 2 |
| #22611648 | 2 |
| #22611558 | 2 |
| #22609986 | 2 |
| #22608032 | 2 |
| C73×#2155 | 2 |
| #13396 | 73 |