Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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. #11729116 | C2 | semidirect |
| 5. #11725608 | C2 | semidirect |
| 6. #11725371 | C2 | semidirect |
| 7. #11725361 | C2 | semidirect |
| 57. C7×D8 | Q16 | semidirect |
| 149. D8 | #1144 | semidirect |
| 190. C7 | #12447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2226 | 2 |
| #11729116 | 2 |
| #11728641 | 2 |
| D8×C7⋊C8 | 2 |
| #11725608 | 2 |
| #11725371 | 2 |
| #11725361 | 2 |
| #12447 | 7 |