Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
248 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 113 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×#1313 | C2 | semidirect |
| 5. #11725317 | C2 | semidirect |
| 6. #11725317 | C2 | semidirect |
| 7. #11725248 | C2 | semidirect |
| 50. #1313 | D7 | semidirect |
| 70. C7×C16 | M16 | semidirect |
| 159. C16 | #1131 | semidirect |
| 183. C7 | #11414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11726827 | 2 |
| #11726825 | 2 |
| #11725823 | 2 |
| C7×#1313 | 2 |
| #11725317 | 2 |
| #11725248 | 2 |
| #11414 | 7 |