Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
460 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 101 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. #11729560 | C2 | semidirect |
| 3. #11729556 | C2 | semidirect |
| 4. #11729371 | C2 | semidirect |
| 5. C2×D4⋊(C7⋊C8) | C2 | semidirect |
| 6. #11728245 | C2 | semidirect |
| 7. #11725517 | C2 | semidirect |
| 369. C7 | #10456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3036 | 2 |
| #11729560 | 2 |
| #11729556 | 2 |
| #11729371 | 2 |
| C2×D4⋊(C7⋊C8) | 2 |
| #11728245 | 2 |
| #11725517 | 2 |
| #10456 | 7 |