Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
414 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 115 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×#89306 | C2 | semidirect |
| 4. #11728309 | C2 | semidirect |
| 6. C7×#1383 | C2 | semidirect |
| 7. #11725536 | C2 | semidirect |
| 20. #89667 | C4 | semidirect |
| 66. #1383 | D7 | semidirect |
| 279. C7 | #12824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89667 | 2 |
| C2×#89313 | 2 |
| C2×#89306 | 2 |
| #11728309 | 2 |
| C2×#89283 | 2 |
| C7×#1383 | 2 |
| #11725536 | 2 |
| #12824 | 7 |