Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
446 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 446 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 |
|---|---|---|
| 2. #11728502 | C2 | semidirect |
| 3. #11728259 | C2 | semidirect |
| 4. #11728256 | C2 | semidirect |
| 5. #11727630 | C2 | semidirect |
| 6. #11727607 | C2 | semidirect |
| 7. C7×#1299 | C2 | semidirect |
| 71. #1299 | 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 |
| #11728502 | 2 |
| #11728259 | 2 |
| #11728256 | 2 |
| #11727630 | 2 |
| #11727607 | 2 |
| C7×#1299 | 2 |
| #10488 | 7 |