Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22581356 | C2 | semidirect |
| 3. #22581291 | C2 | semidirect |
| 4. #22581266 | C2 | semidirect |
| 5. #22581248 | C2 | semidirect |
| 6. #22581240 | C2 | semidirect |
| 7. #22581201 | C2 | semidirect |
| 8. C4×#14555772 | C2 | semidirect |
| 9. #22581031 | C2 | semidirect |
| 10. #22580993 | C2 | semidirect |
| 11. #554×C139 | C2 | semidirect |
| 121. C139 | #3357 | semidirect |
| 124. #554 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581668 | 2 |
| #22581356 | 2 |
| #22581291 | 2 |
| #22581266 | 2 |
| #22581248 | 2 |
| #22581240 | 2 |
| #22581201 | 2 |
| C4×#14555772 | 2 |
| #22581031 | 2 |
| #22580993 | 2 |
| #554×C139 | 2 |
| #3357 | 139 |