Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #22581250 | C2 | semidirect |
| 3. #22581250 | C2 | semidirect |
| 4. #22581240 | C2 | semidirect |
| 5. #22581230 | C2 | semidirect |
| 6. #22580993 | C2 | semidirect |
| 7. #22580989 | C2 | semidirect |
| 8. #22580980 | C2 | semidirect |
| 11. #544×C139 | C2 | semidirect |
| 21. #17984775 | C22 | semidirect |
| 22. #17984775 | C22 | semidirect |
| 23. #17984775 | C22 | semidirect |
| 24. #17984773 | C22 | semidirect |
| 25. #17984773 | C22 | semidirect |
| 26. #17984773 | C22 | semidirect |
| 27. C4⋊(C139⋊C8) | C22 | semidirect |
| 28. C4⋊(C139⋊C8) | C22 | semidirect |
| 34. C4⋊Q8×C139 | C22 | semidirect |
| 36. #125×C139 | C22 | semidirect |
| 44. C2×D556 | Q8 | semidirect |
| 124. C139 | #3081 | semidirect |
| 126. #544 | D139 | semidirect |
| 141. C4⋊Q8 | C2×D139 | semidirect |
| 143. #125 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581427 | 2 |
| #22581250 | 2 |
| #22581240 | 2 |
| #22581230 | 2 |
| #22580993 | 2 |
| #22580989 | 2 |
| #22580980 | 2 |
| #22580957 | 2 |
| C2×#17984762 | 2 |
| #544×C139 | 2 |
| #3081 | 139 |