Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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×#17984863 | C2 | semidirect |
| 2. #22581625 | C2 | semidirect |
| 3. #22581623 | C2 | semidirect |
| 4. #22581329 | C2 | semidirect |
| 5. #22581188 | C2 | semidirect |
| 6. #22581154 | C2 | semidirect |
| 7. #22581099 | C2 | semidirect |
| 8. #22581097 | C2 | semidirect |
| 9. C4×#14555775 | C2 | semidirect |
| 10. #22581018 | C2 | semidirect |
| 11. #460×C139 | C2 | semidirect |
| 58. #14555775 | D4 | semidirect |
| 130. C4×C139 | #135 | semidirect |
| 142. C139 | #3287 | semidirect |
| 150. #460 | D139 | semidirect |
| 276. C4 | #17984863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984863 | 2 |
| #22581625 | 2 |
| #22581623 | 2 |
| #22581329 | 2 |
| #22581188 | 2 |
| #22581154 | 2 |
| #22581099 | 2 |
| #22581097 | 2 |
| C4×#14555775 | 2 |
| #22581018 | 2 |
| #460×C139 | 2 |
| #3287 | 139 |