Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
490 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11736490 | C2 | semidirect |
| 5. #11727300 | C2 | semidirect |
| 6. C7×#1286 | C2 | semidirect |
| 7. #11725546 | C2 | semidirect |
| 23. #89466 | C4 | semidirect |
| 24. #89465 | C4 | semidirect |
| 72. #1286 | D7 | semidirect |
| 117. C2×C7⋊C8 | SD16 | semidirect |
| 325. C7 | #9294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736750 | 2 |
| #11736490 | 2 |
| #11728256 | 2 |
| #11727307 | 2 |
| #11727300 | 2 |
| C7×#1286 | 2 |
| #11725546 | 2 |
| #9294 | 7 |