Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 234 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. #11728635 | C2 | semidirect |
| 3. #11726317 | C2 | semidirect |
| 4. C7×#1331 | C2 | semidirect |
| 5. #11725310 | C2 | semidirect |
| 6. #11725304 | C2 | semidirect |
| 7. #11725276 | C2 | semidirect |
| 50. #1331 | D7 | semidirect |
| 76. C7⋊C16 | M16 | semidirect |
| 203. C7 | #12086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6400 | 2 |
| #11728635 | 2 |
| #11726317 | 2 |
| C7×#1331 | 2 |
| #11725310 | 2 |
| #11725304 | 2 |
| #11725276 | 2 |
| #12086 | 7 |