Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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×#17984865 | C2 | semidirect |
| 2. #22581625 | C2 | semidirect |
| 3. #22581606 | C2 | semidirect |
| 4. #22581327 | C2 | semidirect |
| 5. #22581185 | C2 | semidirect |
| 6. #22581149 | C2 | semidirect |
| 7. #22581114 | C2 | semidirect |
| 8. #22581101 | C2 | semidirect |
| 9. C4×#14555772 | C2 | semidirect |
| 10. #22581018 | C2 | semidirect |
| 11. #462×C139 | C2 | semidirect |
| 60. #14555772 | D4 | semidirect |
| 129. C4×C139 | #135 | semidirect |
| 140. C139 | #3284 | semidirect |
| 147. #462 | D139 | semidirect |
| 272. C4 | #17984865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984865 | 2 |
| #22581625 | 2 |
| #22581606 | 2 |
| #22581327 | 2 |
| #22581185 | 2 |
| #22581149 | 2 |
| #22581114 | 2 |
| #22581101 | 2 |
| C4×#14555772 | 2 |
| #22581018 | 2 |
| #462×C139 | 2 |
| #3284 | 139 |