Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
604 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 85 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. #11733846 | C2 | semidirect |
| 3. #11726430 | C2 | semidirect |
| 4. #11726383 | C2 | semidirect |
| 5. C7×#1270 | C2 | semidirect |
| 6. #11725286 | C2 | semidirect |
| 7. #11725284 | C2 | semidirect |
| 74. #1270 | D7 | semidirect |
| 80. C2×C7×D4 | SD16 | semidirect |
| 113. C2×Dic14 | D8 | semidirect |
| 323. C2×D4 | #1132 | semidirect |
| 435. C7 | #7735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11733846 | 2 |
| #11727412 | 2 |
| #11726430 | 2 |
| #11726383 | 2 |
| C7×#1270 | 2 |
| #11725286 | 2 |
| #11725284 | 2 |
| #7735 | 7 |