Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
428 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 97 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×#1801 | C2 | semidirect |
| 3. C2×Q8⋊(C7⋊C8) | C2 | semidirect |
| 6. #11728244 | C2 | semidirect |
| 7. #11725517 | C2 | semidirect |
| 71. #1801 | D7 | semidirect |
| 350. C7 | #10459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739886 | 2 |
| C7×#1801 | 2 |
| C2×Q8⋊(C7⋊C8) | 2 |
| #11728257 | 2 |
| #11728252 | 2 |
| #11728244 | 2 |
| #11725517 | 2 |
| #10459 | 7 |