Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
296 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 63 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. C7×#1696 | C2 | semidirect |
| 3. #11729141 | C2 | semidirect |
| 4. #11729137 | C2 | semidirect |
| 5. #11725575 | C2 | semidirect |
| 6. #11725273 | C2 | semidirect |
| 7. #11725271 | C2 | semidirect |
| 64. #1696 | D7 | semidirect |
| 271. C7 | #12388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11737401 | 2 |
| C7×#1696 | 2 |
| #11729141 | 2 |
| #11729137 | 2 |
| #11725575 | 2 |
| #11725273 | 2 |
| #11725271 | 2 |
| #12388 | 7 |