Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#17984875 | C2 | semidirect |
| 2. C2×#17984870 | C2 | semidirect |
| 3. C2×#17984864 | C2 | semidirect |
| 4. C22×#14555774 | C2 | semidirect |
| 5. #22581529 | C2 | semidirect |
| 6. #22581522 | C2 | semidirect |
| 7. #22581347 | C2 | semidirect |
| 8. #22581342 | C2 | semidirect |
| 9. #22581337 | C2 | semidirect |
| 10. #22581326 | C2 | semidirect |
| 11. #405×C139 | C2 | semidirect |
| 19. C2×Dic556 | C22 | semidirect |
| 20. C2×Dic556 | C22 | semidirect |
| 25. C2×#14555774 | C22 | semidirect |
| 26. C2×#14555774 | C22 | semidirect |
| 27. C2×#14555774 | C22 | semidirect |
| 29. C2×D1112 | C22 | semidirect |
| 30. #17984842 | C22 | semidirect |
| 33. #17984830 | C22 | semidirect |
| 41. #97×C139 | C22 | semidirect |
| 42. C4×C8×C139 | C22 | semidirect |
| 80. M16×C139 | D4 | semidirect |
| 81. C2×C8×C139 | D4 | semidirect |
| 148. C139 | #3154 | semidirect |
| 160. #405 | D139 | semidirect |
| 190. #97 | C2×D139 | semidirect |
| 191. C4×C8 | C2×D139 | semidirect |
| 226. M16 | D556 | semidirect |
| 227. C2×C8 | D556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984875 | 2 |
| C2×#17984870 | 2 |
| C2×#17984864 | 2 |
| C22×#14555774 | 2 |
| #22581529 | 2 |
| #22581522 | 2 |
| #22581347 | 2 |
| #22581342 | 2 |
| #22581337 | 2 |
| #22581326 | 2 |
| #405×C139 | 2 |
| #3154 | 139 |