Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
204 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 204 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 |
|---|---|---|
| 1. C22×C7×C32 | C2 | semidirect |
| 3. C2×#89242 | C2 | semidirect |
| 4. C22⋊(C7⋊C32) | C2 | semidirect |
| 5. (C2×D7)⋊C32 | C2 | semidirect |
| 6. Dic7⋊C32 | C2 | semidirect |
| 7. #11725395 | C2 | semidirect |
| 38. C7×C32 | D4 | semidirect |
| 42. C22×C32 | D7 | semidirect |
| 116. C32 | C22⋊D7 | semidirect |
| 119. C22×C7 | M64 | semidirect |
| 172. C7 | #13645 | semidirect |
| 178. C22 | #89242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×C32 | 2 |
| C16×C22⋊D7 | 2 |
| C2×#89242 | 2 |
| C22⋊(C7⋊C32) | 2 |
| (C2×D7)⋊C32 | 2 |
| Dic7⋊C32 | 2 |
| #11725395 | 2 |
| #13645 | 7 |