Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22581326 | C2 | semidirect |
| 3. #22581248 | C2 | semidirect |
| 4. #22581244 | C2 | semidirect |
| 5. #22580696 | C2 | semidirect |
| 6. #22580682 | C2 | semidirect |
| 7. Q8⋊C8×C139 | C2 | semidirect |
| 69. Q8×C139 | SD16 | semidirect |
| 98. C139 | #1631 | semidirect |
| 105. Q8⋊C8 | D139 | semidirect |
| 153. Q8 | #14555774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581625 | 2 |
| #22581326 | 2 |
| #22581248 | 2 |
| #22581244 | 2 |
| #22580696 | 2 |
| #22580682 | 2 |
| Q8⋊C8×C139 | 2 |
| #1631 | 139 |