Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
226 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. C7×#1368 | C2 | semidirect |
| 5. #11725319 | C2 | semidirect |
| 6. #11725270 | C2 | semidirect |
| 7. #11725270 | C2 | semidirect |
| 51. #1368 | D7 | semidirect |
| 72. C7×C16 | M16 | semidirect |
| 74. C7⋊C16 | M16 | semidirect |
| 164. C16 | #1131 | semidirect |
| 189. C7 | #12019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×#346 | 2 |
| #11726284 | 2 |
| #11726283 | 2 |
| C7×#1368 | 2 |
| #11725319 | 2 |
| #11725270 | 2 |
| #12019 | 7 |