Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
408 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 1. #22581624 | C2 | semidirect |
| 2. #22581301 | C2 | semidirect |
| 3. #22581277 | C2 | semidirect |
| 4. #22581245 | C2 | semidirect |
| 5. #22581187 | C2 | semidirect |
| 6. #22581148 | C2 | semidirect |
| 7. #22581096 | C2 | semidirect |
| 8. C4×#14555773 | C2 | semidirect |
| 9. D4×C139⋊C8 | C2 | semidirect |
| 10. #22580947 | C2 | semidirect |
| 11. #555×C139 | C2 | semidirect |
| 132. C139 | #3305 | semidirect |
| 134. #555 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581624 | 2 |
| #22581301 | 2 |
| #22581277 | 2 |
| #22581245 | 2 |
| #22581187 | 2 |
| #22581148 | 2 |
| #22581096 | 2 |
| C4×#14555773 | 2 |
| D4×C139⋊C8 | 2 |
| #22580947 | 2 |
| #555×C139 | 2 |
| #3305 | 139 |