Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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×#17984807 | C2 | semidirect |
| 3. #22581288 | C2 | semidirect |
| 4. #22581263 | C2 | semidirect |
| 5. #22581174 | C2 | semidirect |
| 6. #22581111 | C2 | semidirect |
| 8. #22581059 | C2 | semidirect |
| 9. #22581050 | C2 | semidirect |
| 10. #22581007 | C2 | semidirect |
| 131. C139 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581484 | 2 |
| C2×#17984807 | 2 |
| #22581288 | 2 |
| #22581263 | 2 |
| #22581174 | 2 |
| #22581111 | 2 |
| #22581091 | 2 |
| #22581059 | 2 |
| #22581050 | 2 |
| #22581007 | 2 |
| #481×C139 | 2 |
| #3117 | 139 |