Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
224 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 91 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. #11726802 | C2 | semidirect |
| 4. C7×C8×C16 | C2 | semidirect |
| 5. #11725312 | C2 | semidirect |
| 7. #11725245 | C2 | semidirect |
| 51. C8×C16 | D7 | semidirect |
| 73. C7×C16 | SD16 | semidirect |
| 107. C7×C8 | M32 | semidirect |
| 168. C16 | #1132 | semidirect |
| 191. C8 | #6372 | semidirect |
| 194. C7 | #12051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11726809 | 2 |
| #11726802 | 2 |
| C8×#1132 | 2 |
| C7×C8×C16 | 2 |
| #11725312 | 2 |
| #11725309 | 2 |
| #11725245 | 2 |
| #12051 | 7 |