Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22611691 | C2 | semidirect |
| 3. C2×#17988404 | C2 | semidirect |
| 4. #22610844 | C2 | semidirect |
| 6. #22608024 | C2 | semidirect |
| 161. C73 | #13440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556535 | 2 |
| #22611691 | 2 |
| C2×#17988404 | 2 |
| #22610844 | 2 |
| #22610842 | 2 |
| #22608024 | 2 |
| C2×#361×C73 | 2 |
| #13440 | 73 |