Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 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. #22581673 | C2 | semidirect |
| 3. #22581304 | C2 | semidirect |
| 4. #22581295 | C2 | semidirect |
| 5. #22581234 | C2 | semidirect |
| 6. #22581194 | C2 | semidirect |
| 7. #22581164 | C2 | semidirect |
| 8. #22581117 | C2 | semidirect |
| 9. C4×#14555774 | C2 | semidirect |
| 10. #22580950 | C2 | semidirect |
| 11. C8×D4×C139 | C2 | semidirect |
| 125. C139 | #3302 | semidirect |
| 136. C8×D4 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581673 | 2 |
| #22581608 | 2 |
| #22581304 | 2 |
| #22581295 | 2 |
| #22581234 | 2 |
| #22581194 | 2 |
| #22581164 | 2 |
| #22581117 | 2 |
| C4×#14555774 | 2 |
| #22580950 | 2 |
| C8×D4×C139 | 2 |
| #3302 | 139 |