Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
3798 conjugacy classes of subgroups; only the 1179 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 1179 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. C2×#89992 | C2 | semidirect |
| 3. #11740619 | C2 | direct (N × H) |
| 4. C2×#89709 | C2 | semidirect |
| 7. C2×C7×#127 | C4 | semidirect |
| 11. #89992 | C22 | semidirect |
| 13. #89709 | C22 | semidirect |
| 18. C22×C7×D4 | C2×C4 | semidirect |
| 24. C7×#127 | C2×C4 | semidirect |
| 25. C2×C42×C7 | C2×C4 | semidirect |
| 42. C2×C7×D4 | C22×C4 | semidirect |
| 50. C42×C7 | C22×C4 | semidirect |
| 54. C2×#127 | Dic7 | semidirect |
| 80. C22×D4 | C2×Dic7 | semidirect |
| 86. #127 | C2×Dic7 | semidirect |
| 89. C2×C42 | C2×Dic7 | semidirect |
| 110. C2×D4 | C22×Dic7 | semidirect |
| 119. C42 | C22×Dic7 | semidirect |
| 121. C2×C7 | #2380 | semidirect |
| 140. C7 | C2×#2380 | semidirect |
| 152. C2 | #11740619 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#127 | 2 |
| C2×#89992 | 2 |
| #11740619 | 2 |
| C2×#89709 | 2 |
| C2×#2380 | 7 |