Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. #22581673 | C2 | semidirect |
| 2. #22581303 | C2 | semidirect |
| 3. #22581291 | C2 | semidirect |
| 4. #22581233 | C2 | semidirect |
| 5. #22581192 | C2 | semidirect |
| 6. #22581160 | C2 | semidirect |
| 7. #22581115 | C2 | semidirect |
| 8. C4×#14555773 | C2 | semidirect |
| 9. D4×C139⋊C8 | C2 | semidirect |
| 10. #22580949 | C2 | semidirect |
| 125. C139 | #3302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581673 | 2 |
| #22581303 | 2 |
| #22581291 | 2 |
| #22581233 | 2 |
| #22581192 | 2 |
| #22581160 | 2 |
| #22581115 | 2 |
| C4×#14555773 | 2 |
| D4×C139⋊C8 | 2 |
| #22580949 | 2 |
| #547×C139 | 2 |
| #3302 | 139 |