Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
760 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#17984873 | C2 | semidirect |
| 3. #22581130 | C2 | direct (N × H) |
| 4. C2×#17984770 | C2 | semidirect |
| 5. C2×#17984759 | C2 | semidirect |
| 6. C2×#124×C139 | C2 | semidirect |
| 15. #17984873 | C22 | semidirect |
| 18. C2×#14555769 | C22 | semidirect |
| 19. #17984770 | C22 | semidirect |
| 20. #17984759 | C22 | semidirect |
| 21. C22×Q8×C139 | C22 | semidirect |
| 24. #124×C139 | C22 | semidirect |
| 26. C2×C42×C139 | C22 | semidirect |
| 47. #14555769 | C23 | semidirect |
| 53. C2×Q8×C139 | C23 | semidirect |
| 63. C42×C139 | C23 | semidirect |
| 116. C2×C139 | #455 | semidirect |
| 119. C139 | C2×#455 | semidirect |
| 123. C2×#124 | D139 | semidirect |
| 132. C22×Q8 | C2×D139 | semidirect |
| 142. #124 | C2×D139 | semidirect |
| 144. C2×C42 | C2×D139 | semidirect |
| 159. C2×Q8 | C22×D139 | semidirect |
| 183. C42 | C22×D139 | semidirect |
| 237. C2 | #22581130 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984887 | 2 |
| C2×#17984873 | 2 |
| #22581130 | 2 |
| C2×#17984770 | 2 |
| C2×#17984759 | 2 |
| C2×#124×C139 | 2 |
| C2×#455 | 139 |