Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
238 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11725806 | C2 | semidirect |
| 3. C7×C8×C16 | C2 | semidirect |
| 4. #11725310 | C2 | semidirect |
| 5. #11725306 | C2 | semidirect |
| 35. C8×C16 | D7 | semidirect |
| 52. C7×C16 | M16 | semidirect |
| 75. C7×C8 | D16 | semidirect |
| 119. C16 | #1131 | semidirect |
| 137. C8 | D112 | semidirect |
| 140. C7 | #12081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D112 | 2 |
| #11725806 | 2 |
| C7×C8×C16 | 2 |
| #11725310 | 2 |
| #11725306 | 2 |
| #12081 | 7 |