Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
502 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11736782 | C2 | semidirect |
| 3. #11728555 | C2 | semidirect |
| 4. #11728527 | C2 | semidirect |
| 5. #11728519 | C2 | semidirect |
| 6. C7×#1302 | C2 | semidirect |
| 7. #11725468 | C2 | semidirect |
| 75. #1302 | D7 | semidirect |
| 312. C7 | #9007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736782 | 2 |
| #11735944 | 2 |
| #11728555 | 2 |
| #11728527 | 2 |
| #11728519 | 2 |
| C7×#1302 | 2 |
| #11725468 | 2 |
| #9007 | 7 |