Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
242 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. C7×#1372 | C2 | semidirect |
| 4. #11725307 | C2 | semidirect |
| 5. #11725276 | C2 | semidirect |
| 39. #1372 | D7 | semidirect |
| 58. C7×C16 | M16 | semidirect |
| 60. C7⋊C16 | M16 | semidirect |
| 138. C16 | #1131 | semidirect |
| 161. C7 | #12023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D7×C16 | 2 |
| #11726323 | 2 |
| C7×#1372 | 2 |
| #11725307 | 2 |
| #11725276 | 2 |
| #12023 | 7 |