Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
930 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 235 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. C22×#6374 | C2 | semidirect |
| 2. C22×D112 | C2 | semidirect |
| 3. C2×#89468 | C2 | semidirect |
| 4. C2×#89467 | C2 | semidirect |
| 5. C2×C7×#346 | C2 | semidirect |
| 6. #11726835 | C2 | direct (N × H) |
| 17. C2×#6374 | C22 | semidirect |
| 19. C2×D112 | C22 | semidirect |
| 21. #89468 | C22 | semidirect |
| 23. #89467 | C22 | semidirect |
| 24. C7×#346 | C22 | semidirect |
| 52. C2×C7×C16 | D4 | semidirect |
| 63. C2×#346 | D7 | semidirect |
| 100. C7×C16 | C2×D4 | semidirect |
| 118. #346 | C2×D7 | semidirect |
| 175. C2×C16 | D28 | semidirect |
| 229. C16 | C2×D28 | semidirect |
| 230. C2×C7 | #2250 | semidirect |
| 263. C7 | C2×#2250 | semidirect |
| 280. C2 | #11726835 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6374 | 2 |
| C22×D112 | 2 |
| C2×#89468 | 2 |
| C2×#89467 | 2 |
| C2×C7×#346 | 2 |
| #11726835 | 2 |
| C2×#2250 | 7 |