Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1022 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 267 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×D112 | C2 | semidirect |
| 2. C2×#89467 | C2 | semidirect |
| 3. C2×C4×C7×C16 | C2 | semidirect |
| 4. #11726814 | C2 | direct (N × H) |
| 11. C2×D112 | C22 | semidirect |
| 13. #89467 | C22 | semidirect |
| 14. C4×C7×C16 | C22 | semidirect |
| 28. C2×C7×C16 | D4 | semidirect |
| 36. C2×C4×C16 | D7 | semidirect |
| 56. C7×C16 | C2×D4 | semidirect |
| 66. C4×C16 | C2×D7 | semidirect |
| 71. C2×C4×C7 | D16 | semidirect |
| 97. C2×C16 | D28 | semidirect |
| 108. C4×C7 | C2×D16 | semidirect |
| 130. C16 | C2×D28 | semidirect |
| 131. C2×C7 | #2246 | semidirect |
| 143. C2×C4 | D112 | semidirect |
| 152. C7 | C2×#2246 | semidirect |
| 160. C4 | C2×D112 | semidirect |
| 164. C2 | #11726814 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D112 | 2 |
| C2×#89467 | 2 |
| C2×C4×C7×C16 | 2 |
| #11726814 | 2 |
| C2×#2246 | 7 |