Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 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. #22581682 | C2 | semidirect |
| 3. #22581309 | C2 | semidirect |
| 5. #22581256 | C2 | semidirect |
| 6. #22581238 | C2 | semidirect |
| 7. #22581177 | C2 | semidirect |
| 9. C8×Dic278 | C2 | semidirect |
| 10. #22581038 | C2 | semidirect |
| 11. C4×Q16×C139 | C2 | semidirect |
| 117. C139 | #3365 | semidirect |
| 128. C4×Q16 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581688 | 2 |
| #22581682 | 2 |
| #22581309 | 2 |
| #22581300 | 2 |
| #22581256 | 2 |
| #22581238 | 2 |
| #22581177 | 2 |
| #22581153 | 2 |
| C8×Dic278 | 2 |
| #22581038 | 2 |
| C4×Q16×C139 | 2 |
| #3365 | 139 |