Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
492 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 135 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×Q16×D139 | C2 | semidirect |
| 4. #22581212 | C2 | semidirect |
| 5. #22581211 | C2 | semidirect |
| 6. #22581210 | C2 | semidirect |
| 7. #22581209 | C2 | semidirect |
| 8. #22581208 | C2 | semidirect |
| 9. #106×D139 | C2 | semidirect |
| 10. #103×D139 | C2 | semidirect |
| 11. #470×C139 | C2 | semidirect |
| 14. C2×Dic556 | C22 | semidirect |
| 15. C2×#14555775 | C22 | semidirect |
| 31. #17984774 | C22 | semidirect |
| 32. #17984773 | C22 | semidirect |
| 33. #17984767 | C22 | semidirect |
| 34. #17984766 | C22 | semidirect |
| 35. #17984765 | C22 | semidirect |
| 36. C2×Q16×C139 | C22 | semidirect |
| 39. #106×C139 | C22 | semidirect |
| 40. #103×C139 | C22 | semidirect |
| 135. D139 | #470 | direct (N × H) |
| 136. C139 | C2×#470 | semidirect |
| 146. #470 | D139 | direct (N × H) |
| 154. C2×Q16 | C2×D139 | semidirect |
| 173. #106 | C2×D139 | semidirect |
| 177. #103 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D139 | 2 |
| C2×M16×D139 | 2 |
| C22⋊Q8×D139 | 2 |
| #22581212 | 2 |
| #22581211 | 2 |
| #22581210 | 2 |
| #22581209 | 2 |
| #22581208 | 2 |
| #106×D139 | 2 |
| #103×D139 | 2 |
| #470×C139 | 2 |
| C2×#470 | 139 |