Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 1. C2×#89688 | C2 | semidirect |
| 2. #11739244 | C2 | semidirect |
| 3. #11739227 | C2 | semidirect |
| 4. C7×#2248 | C2 | semidirect |
| 5. #11729234 | C2 | semidirect |
| 6. #11729066 | C2 | semidirect |
| 7. #11729044 | C2 | semidirect |
| 8. #11726815 | C2 | semidirect |
| 9. C4×D7×C16 | C2 | semidirect |
| 78. D7×C16 | D4 | semidirect |
| 84. #2248 | D7 | semidirect |
| 237. C4×C7 | #508 | semidirect |
| 321. C7 | #33713 | semidirect |
| 333. C4 | #89688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89688 | 2 |
| #11739244 | 2 |
| #11739227 | 2 |
| C7×#2248 | 2 |
| #11729234 | 2 |
| #11729066 | 2 |
| #11729044 | 2 |
| #11726815 | 2 |
| C4×D7×C16 | 2 |
| #33713 | 7 |