Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2502 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 667 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 |
|---|---|---|
| 1. C22×#6439 | C2 | semidirect |
| 2. C2×C7×#384 | C2 | semidirect |
| 3. C2×#89766 | C2 | semidirect |
| 5. C2×#89755 | C2 | semidirect |
| 6. #11731819 | C2 | direct (N × H) |
| 16. C2×#6439 | C22 | semidirect |
| 17. C7×#384 | C22 | semidirect |
| 20. #89766 | C22 | semidirect |
| 22. #89755 | C22 | semidirect |
| 35. C2×C42×C7 | D4 | semidirect |
| 53. C2×#384 | D7 | semidirect |
| 76. C42×C7 | C2×D4 | semidirect |
| 94. #384 | C2×D7 | semidirect |
| 141. C2×C42 | D28 | semidirect |
| 185. C42 | C2×D28 | semidirect |
| 186. C2×C7 | #2823 | semidirect |
| 215. C7 | C2×#2823 | semidirect |
| 231. C2 | #11731819 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6439 | 2 |
| C2×C7×#384 | 2 |
| C2×#89766 | 2 |
| C2×#89763 | 2 |
| C2×#89755 | 2 |
| #11731819 | 2 |
| C2×#2823 | 7 |