Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
512 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11740761 | C2 | semidirect |
| 3. #11736800 | C2 | semidirect |
| 4. C7×#1530 | C2 | semidirect |
| 5. #11727592 | C2 | semidirect |
| 6. #11727552 | C2 | semidirect |
| 7. #11725561 | C2 | semidirect |
| 88. #1530 | D7 | semidirect |
| 375. C7 | #10028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740761 | 2 |
| #11740755 | 2 |
| #11736800 | 2 |
| C7×#1530 | 2 |
| #11727592 | 2 |
| #11727552 | 2 |
| #11725561 | 2 |
| #10028 | 7 |