Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
546 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11733844 | C2 | semidirect |
| 3. #11726383 | C2 | semidirect |
| 4. #11726383 | C2 | semidirect |
| 5. C7×#1270 | C2 | semidirect |
| 6. #11725284 | C2 | semidirect |
| 7. #11725283 | C2 | semidirect |
| 72. #1270 | D7 | semidirect |
| 127. C4⋊Dic7 | D8 | semidirect |
| 419. C7 | #7740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11733844 | 2 |
| #11727412 | 2 |
| #11726383 | 2 |
| C7×#1270 | 2 |
| #11725284 | 2 |
| #11725283 | 2 |
| #7740 | 7 |