Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
442 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 131 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×#89258 | C2 | semidirect |
| 3. #11725593 | C2 | direct (N × H) |
| 13. #89258 | C22 | semidirect |
| 179. C2×C7 | #1359 | semidirect |
| 206. C7 | C2×#1359 | semidirect |
| 223. C2 | #11725593 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#492 | 2 |
| C2×#89258 | 2 |
| #11725593 | 2 |
| C2×#1359 | 7 |