Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
220 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 73 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. #11728659 | C2 | semidirect |
| 4. C7×#1332 | C2 | semidirect |
| 6. #11725304 | C2 | semidirect |
| 7. #11725275 | C2 | semidirect |
| 49. #1332 | D7 | semidirect |
| 75. C7⋊C16 | M16 | semidirect |
| 194. C7 | #12084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6402 | 2 |
| #11728659 | 2 |
| #11726317 | 2 |
| C7×#1332 | 2 |
| #11725310 | 2 |
| #11725304 | 2 |
| #11725275 | 2 |
| #12084 | 7 |