Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
212 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 71 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. C4×D112 | C2 | semidirect |
| 3. C7×#1397 | C2 | semidirect |
| 4. #11725402 | C2 | semidirect |
| 5. #11725398 | C2 | semidirect |
| 13. D224 | C4 | semidirect |
| 23. D112 | C2×C4 | semidirect |
| 25. C7×C32 | C2×C4 | semidirect |
| 30. #1397 | D7 | semidirect |
| 71. C32 | C4×D7 | semidirect |
| 105. C7 | #13654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D224 | 2 |
| C4×D112 | 2 |
| C7×#1397 | 2 |
| #11725402 | 2 |
| #11725398 | 2 |
| #13654 | 7 |