Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1722 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1722 conjugacy classes of subgroups — too many to draw. Only its 251 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×#89848 | C2 | semidirect |
| 3. C2×#89780 | C2 | semidirect |
| 4. #11729661 | C2 | direct (N × H) |
| 5. C2×#89339 | C2 | semidirect |
| 6. C2×D4⋊(C7⋊C8) | C2 | semidirect |
| 16. C2×#6432 | C22 | semidirect |
| 19. #89848 | C22 | semidirect |
| 21. #89780 | C22 | semidirect |
| 23. C2×C4⋊(C7⋊C8) | C22 | semidirect |
| 24. C2×C4×C7⋊C8 | C22 | semidirect |
| 25. #89339 | C22 | semidirect |
| 26. D4⋊(C7⋊C8) | C22 | semidirect |
| 61. #6432 | C23 | semidirect |
| 65. C4⋊(C7⋊C8) | C23 | semidirect |
| 67. C4×C7⋊C8 | C23 | semidirect |
| 92. C2×C7×D4 | SD16 | semidirect |
| 160. C7×D4 | C2×SD16 | semidirect |
| 258. C2×D4 | #1142 | semidirect |
| 286. C2×C7 | #1629 | semidirect |
| 310. D4 | C2×#1142 | semidirect |
| 327. C7 | C2×#1629 | semidirect |
| 348. C2 | #11729661 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×D42 | 2 |
| C2×#89848 | 2 |
| C2×#89780 | 2 |
| #11729661 | 2 |
| C2×#89339 | 2 |
| C2×D4⋊(C7⋊C8) | 2 |
| C2×#1629 | 7 |