Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11739452 | C2 | semidirect |
| 3. C7×#2143 | C2 | semidirect |
| 4. #11729834 | C2 | semidirect |
| 5. #11728472 | C2 | semidirect |
| 6. #11725622 | C2 | semidirect |
| 7. #11725536 | C2 | semidirect |
| 55. C2×C7×C16 | D4 | semidirect |
| 68. C2×C7⋊C16 | D4 | semidirect |
| 74. #2143 | D7 | semidirect |
| 217. C2×C16 | C22⋊D7 | semidirect |
| 338. C7 | #13076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741361 | 2 |
| #11739452 | 2 |
| C7×#2143 | 2 |
| #11729834 | 2 |
| #11728472 | 2 |
| #11725622 | 2 |
| #11725536 | 2 |
| #13076 | 7 |