Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22611705 | C2 | semidirect |
| 3. #22611651 | C2 | semidirect |
| 6. #22608033 | C2 | semidirect |
| 7. C2×#362×C73 | C2 | semidirect |
| 162. C2×#362 | 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 |
| #22611705 | 2 |
| #22611651 | 2 |
| #22611560 | 2 |
| #22609986 | 2 |
| #22608033 | 2 |
| C2×#362×C73 | 2 |
| #13397 | 73 |