Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
918 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 918 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×#6374 | C2 | semidirect |
| 2. C2×#89471 | C2 | semidirect |
| 4. C2×C4×C7×C16 | C2 | semidirect |
| 5. #11726815 | C2 | direct (N × H) |
| 15. C2×#6374 | C22 | semidirect |
| 17. #89471 | C22 | semidirect |
| 20. C4×C7×C16 | C22 | semidirect |
| 43. C2×C7×C16 | D4 | semidirect |
| 52. C2×C4×C16 | D7 | semidirect |
| 81. C7×C16 | C2×D4 | semidirect |
| 96. C4×C16 | C2×D7 | semidirect |
| 101. C2×C4×C7 | SD32 | semidirect |
| 141. C2×C16 | D28 | semidirect |
| 152. C4×C7 | C2×SD32 | semidirect |
| 184. C16 | C2×D28 | semidirect |
| 185. C2×C7 | #2248 | semidirect |
| 202. C2×C4 | #6374 | semidirect |
| 211. C7 | C2×#2248 | semidirect |
| 220. C4 | C2×#6374 | semidirect |
| 224. C2 | #11726815 | 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 |
| C2×#89471 | 2 |
| C2×#89467 | 2 |
| C2×C4×C7×C16 | 2 |
| #11726815 | 2 |
| C2×#2248 | 7 |