Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#17984862 | C2 | semidirect |
| 2. #22581624 | C2 | semidirect |
| 3. #22581329 | C2 | semidirect |
| 4. #22581187 | C2 | semidirect |
| 5. #22581153 | C2 | semidirect |
| 6. #22581150 | C2 | semidirect |
| 7. #22581098 | C2 | semidirect |
| 8. #22581096 | C2 | semidirect |
| 9. C4×#14555775 | C2 | semidirect |
| 10. D4×C139⋊C8 | C2 | semidirect |
| 11. #550×C139 | C2 | semidirect |
| 51. #14555775 | D4 | semidirect |
| 131. C4×C139 | #135 | semidirect |
| 142. C139 | #3287 | semidirect |
| 146. #550 | D139 | semidirect |
| 276. C4 | #17984862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984862 | 2 |
| #22581624 | 2 |
| #22581329 | 2 |
| #22581187 | 2 |
| #22581153 | 2 |
| #22581150 | 2 |
| #22581098 | 2 |
| #22581096 | 2 |
| C4×#14555775 | 2 |
| D4×C139⋊C8 | 2 |
| #550×C139 | 2 |
| #3287 | 139 |