Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
918 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 179 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×#89686 | C2 | semidirect |
| 2. #11739244 | C2 | semidirect |
| 3. D7×#493 | C2 | semidirect |
| 4. C7×#2248 | C2 | semidirect |
| 5. #11729235 | C2 | semidirect |
| 6. #11729067 | C2 | semidirect |
| 7. #11729044 | C2 | semidirect |
| 8. #11726814 | C2 | semidirect |
| 9. C4×#6372 | C2 | semidirect |
| 16. C2×C7×SD32 | C22 | semidirect |
| 17. C7×#494 | C22 | semidirect |
| 20. #89963 | C22 | semidirect |
| 21. C2×#6402 | C22 | semidirect |
| 24. C2×#6400 | C22 | semidirect |
| 28. C2×D112 | C22 | semidirect |
| 31. #89467 | C22 | semidirect |
| 33. C4×C7×C16 | C22 | semidirect |
| 34. #89297 | C22 | semidirect |
| 35. C4×C7⋊C16 | C22 | semidirect |
| 78. #6372 | D4 | semidirect |
| 84. #2248 | D7 | semidirect |
| 130. C7×C16 | C2×D4 | semidirect |
| 131. C7⋊C16 | C2×D4 | semidirect |
| 140. C2×SD32 | C2×D7 | semidirect |
| 146. #494 | C2×D7 | semidirect |
| 157. C4×C16 | C2×D7 | semidirect |
| 244. C4×C7 | #509 | semidirect |
| 292. C16 | D4×D7 | semidirect |
| 332. C7 | #33717 | semidirect |
| 346. C4 | #89686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89686 | 2 |
| #11739244 | 2 |
| D7×#493 | 2 |
| C7×#2248 | 2 |
| #11729235 | 2 |
| #11729067 | 2 |
| #11729044 | 2 |
| #11726814 | 2 |
| C4×#6372 | 2 |
| #33717 | 7 |