Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
700 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#17984872 | C2 | semidirect |
| 2. C22×#14555775 | C2 | semidirect |
| 3. #22581524 | C2 | semidirect |
| 4. #22581115 | C2 | semidirect |
| 5. #22581109 | C2 | semidirect |
| 6. #22580962 | C2 | semidirect |
| 7. #22580949 | C2 | semidirect |
| 8. #22580920 | C2 | semidirect |
| 140. C139 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984872 | 2 |
| C22×#14555775 | 2 |
| #22581524 | 2 |
| #22581115 | 2 |
| #22581109 | 2 |
| #22580962 | 2 |
| #22580949 | 2 |
| #22580920 | 2 |
| C2×2−1+4×C139 | 2 |
| #3011 | 139 |