Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
510 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 3. C2×#89307 | C2 | semidirect |
| 4. C7×#1375 | C2 | semidirect |
| 5. #11725469 | C2 | semidirect |
| 17. (C2×D7)⋊C16 | C4 | semidirect |
| 39. C2×C7×C16 | C2×C4 | semidirect |
| 45. C2×C7⋊C16 | C2×C4 | semidirect |
| 51. #1375 | D7 | semidirect |
| 151. C2×C16 | C4×D7 | semidirect |
| 164. C2×D7 | #347 | semidirect |
| 241. C7 | #12605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×#97 | 2 |
| #11729185 | 2 |
| C2×#89307 | 2 |
| C7×#1375 | 2 |
| #11725469 | 2 |
| #12605 | 7 |