Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
520 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 185 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×#17984850 | C2 | semidirect |
| 2. C22×C8×D139 | C2 | semidirect |
| 4. #22581023 | C2 | semidirect |
| 5. #22581018 | C2 | semidirect |
| 6. #22580919 | C2 | semidirect |
| 7. #22580916 | C2 | semidirect |
| 8. #22580909 | C2 | semidirect |
| 9. #424×C139 | C2 | semidirect |
| 14. C2×#14555768 | C22 | semidirect |
| 19. C2×C8×D139 | C22 | semidirect |
| 26. (C2×D139)⋊C8 | C22 | semidirect |
| 27. #17984753 | C22 | semidirect |
| 28. C4×C139⋊C8 | C22 | semidirect |
| 32. C4⋊C8×C139 | C22 | semidirect |
| 48. C2×C139⋊C8 | D4 | semidirect |
| 101. C2×D139 | #131 | semidirect |
| 113. C139 | #2929 | semidirect |
| 120. #424 | D139 | semidirect |
| 142. C4⋊C8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984850 | 2 |
| C22×C8×D139 | 2 |
| #22581465 | 2 |
| #22581023 | 2 |
| #22581018 | 2 |
| #22580919 | 2 |
| #22580916 | 2 |
| #22580909 | 2 |
| #424×C139 | 2 |
| #2929 | 139 |