Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
994 conjugacy classes of subgroups; only the 475 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 475 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×C7×C82 | C2 | semidirect |
| 3. C2×#89250 | C2 | semidirect |
| 4. #11725804 | C2 | direct (N × H) |
| 12. C7×C82 | C22 | semidirect |
| 13. #89250 | C22 | semidirect |
| 32. C2×C82 | D7 | semidirect |
| 39. C2×C7×C8 | M16 | semidirect |
| 56. C82 | C2×D7 | semidirect |
| 67. C7×C8 | C2×M16 | semidirect |
| 99. C2×C8 | #1131 | semidirect |
| 105. C2×C7 | #1455 | semidirect |
| 119. C8 | C2×#1131 | semidirect |
| 120. C7 | C2×#1455 | semidirect |
| 129. C2 | #11725804 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1131 | 2 |
| C2×C7×C82 | 2 |
| C2×#89250 | 2 |
| #11725804 | 2 |
| C2×#1455 | 7 |