Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
422 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 422 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. C7×#1944 | C2 | semidirect |
| 4. #11728350 | C2 | semidirect |
| 6. #11725527 | C2 | semidirect |
| 7. #11725470 | C2 | semidirect |
| 27. #89283 | C4 | semidirect |
| 55. C7×#106 | C2×C4 | semidirect |
| 69. #6386 | C2×C4 | semidirect |
| 76. #1944 | D7 | semidirect |
| 121. Dic28 | C4⋊C4 | semidirect |
| 123. D56 | C4⋊C4 | semidirect |
| 219. #106 | C4×D7 | semidirect |
| 337. C7 | #12943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735939 | 2 |
| C7×#1944 | 2 |
| #11728352 | 2 |
| #11728350 | 2 |
| C2×#89283 | 2 |
| #11725527 | 2 |
| #11725470 | 2 |
| #12943 | 7 |