Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1722 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1722 conjugacy classes of subgroups — too many to draw. Only its 219 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×C7×#492 | C2 | semidirect |
| 3. C2×#89856 | C2 | semidirect |
| 4. C2×#89339 | C2 | semidirect |
| 5. #11729020 | C2 | direct (N × H) |
| 6. C2×#89254 | C2 | semidirect |
| 9. C2×C7×C4⋊Q8 | C22 | semidirect |
| 18. C7×#492 | C22 | semidirect |
| 19. C2×C4×C7×C8 | C22 | semidirect |
| 21. #89856 | C22 | semidirect |
| 24. C2×C4⋊(C7⋊C8) | C22 | semidirect |
| 25. #89339 | C22 | semidirect |
| 26. #89254 | C22 | semidirect |
| 44. C7×C4⋊Q8 | C23 | semidirect |
| 63. C4×C7×C8 | C23 | semidirect |
| 67. C4⋊(C7⋊C8) | C23 | semidirect |
| 69. C2×#492 | D7 | semidirect |
| 100. C2×D28 | SD16 | semidirect |
| 126. C2×C4⋊Q8 | C2×D7 | semidirect |
| 132. #492 | C2×D7 | semidirect |
| 138. C2×C4×C8 | C2×D7 | semidirect |
| 173. D28 | C2×SD16 | semidirect |
| 196. C4⋊Q8 | C22×D7 | semidirect |
| 218. C4×C8 | C22×D7 | semidirect |
| 285. C2×C7 | #1629 | semidirect |
| 327. C7 | C2×#1629 | semidirect |
| 348. C2 | #11729020 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90408 | 2 |
| C2×C7×#492 | 2 |
| C2×#89856 | 2 |
| C2×#89339 | 2 |
| #11729020 | 2 |
| C2×#89254 | 2 |
| C2×#1629 | 7 |