Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
712 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 147 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×#89683 | C2 | semidirect |
| 2. #11737051 | C2 | semidirect |
| 3. C4×C7×D16 | C2 | semidirect |
| 4. #11728644 | C2 | semidirect |
| 5. #11727083 | C2 | semidirect |
| 6. #11726948 | C2 | semidirect |
| 7. #11726945 | C2 | semidirect |
| 8. #11726816 | C2 | semidirect |
| 9. #11726809 | C2 | semidirect |
| 11. C2×D7×D8 | C22 | semidirect |
| 14. C4×C7×D8 | C22 | semidirect |
| 15. C2×#6401 | C22 | semidirect |
| 19. C2×Dic56 | C22 | semidirect |
| 20. C2×#6374 | C22 | semidirect |
| 22. C2×#6372 | C22 | semidirect |
| 23. #89659 | C22 | semidirect |
| 27. #89468 | C22 | semidirect |
| 29. C7×#366 | C22 | semidirect |
| 30. C7×#357 | C22 | semidirect |
| 31. C4×C7×C16 | C22 | semidirect |
| 32. (C2×D7)⋊C16 | C22 | semidirect |
| 33. #89287 | C22 | semidirect |
| 34. #89286 | C22 | semidirect |
| 35. C4⋊(C7⋊C16) | C22 | semidirect |
| 59. C7×D16 | D4 | semidirect |
| 83. C4×D16 | D7 | semidirect |
| 144. C4×D8 | C2×D7 | semidirect |
| 146. #366 | C2×D7 | semidirect |
| 150. #357 | C2×D7 | semidirect |
| 152. C4×C16 | C2×D7 | semidirect |
| 210. D16 | D28 | semidirect |
| 318. C7 | #33839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89683 | 2 |
| #11737051 | 2 |
| C4×C7×D16 | 2 |
| #11728644 | 2 |
| #11727083 | 2 |
| #11726948 | 2 |
| #11726945 | 2 |
| #11726816 | 2 |
| #11726809 | 2 |
| #33839 | 7 |