Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
234 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 75 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. #11726317 | C2 | semidirect |
| 3. C7×#1372 | C2 | semidirect |
| 4. #11725304 | C2 | semidirect |
| 5. #11725277 | C2 | semidirect |
| 33. #1372 | D7 | semidirect |
| 50. C7×C16 | M16 | semidirect |
| 115. C16 | #1131 | semidirect |
| 135. C7 | #12086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D112 | 2 |
| #11726317 | 2 |
| C7×#1372 | 2 |
| #11725304 | 2 |
| #11725277 | 2 |
| #12086 | 7 |