Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
442 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 151 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×C7×#108 | C2 | semidirect |
| 4. C2×#89256 | C2 | semidirect |
| 5. #11725535 | C2 | semidirect |
| 18. #89292 | C4 | semidirect |
| 38. C7×#108 | C2×C4 | semidirect |
| 49. C2×C7⋊C16 | C2×C4 | semidirect |
| 53. C4×#108 | D7 | semidirect |
| 145. #108 | C4×D7 | semidirect |
| 226. C7 | #12640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6467 | 2 |
| C4×C7×#108 | 2 |
| C2×#89292 | 2 |
| C2×#89256 | 2 |
| #11725535 | 2 |
| #12640 | 7 |