Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C2×#17984864 | C2 | semidirect |
| 2. C22×#14555768 | C2 | semidirect |
| 3. #22581465 | C2 | semidirect |
| 4. #22581212 | C2 | semidirect |
| 5. #22581207 | C2 | semidirect |
| 6. #22581200 | C2 | semidirect |
| 7. #22580947 | C2 | semidirect |
| 8. #427×C139 | C2 | semidirect |
| 12. C2×Dic556 | C22 | semidirect |
| 13. C2×#14555774 | C22 | semidirect |
| 14. C2×D1112 | C22 | semidirect |
| 24. #17984765 | C22 | semidirect |
| 25. #17984762 | C22 | semidirect |
| 28. #107×C139 | C22 | semidirect |
| 29. #106×C139 | C22 | semidirect |
| 54. C2×C8×C139 | D4 | semidirect |
| 105. C139 | #3054 | semidirect |
| 113. #427 | D139 | semidirect |
| 132. #107 | C2×D139 | semidirect |
| 133. #106 | C2×D139 | semidirect |
| 157. C2×C8 | D556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984864 | 2 |
| C22×#14555768 | 2 |
| #22581465 | 2 |
| #22581212 | 2 |
| #22581207 | 2 |
| #22581200 | 2 |
| #22580947 | 2 |
| #427×C139 | 2 |
| #3054 | 139 |