Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
446 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 446 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 |
|---|---|---|
| 2. C7×#1574 | C2 | semidirect |
| 3. #11728528 | C2 | semidirect |
| 4. #11728515 | C2 | semidirect |
| 5. #11728275 | C2 | semidirect |
| 6. #11728259 | C2 | semidirect |
| 7. #11725549 | C2 | semidirect |
| 67. #1574 | D7 | semidirect |
| 318. C7 | #10488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736748 | 2 |
| C7×#1574 | 2 |
| #11728528 | 2 |
| #11728515 | 2 |
| #11728275 | 2 |
| #11728259 | 2 |
| #11725549 | 2 |
| #10488 | 7 |