Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 406 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 |
|---|---|---|
| 4. #11728263 | C2 | semidirect |
| 5. #11728255 | C2 | semidirect |
| 6. #11728245 | C2 | semidirect |
| 7. #11725517 | C2 | semidirect |
| 334. C7 | #10461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739741 | 2 |
| C7×#1800 | 2 |
| C2×D4⋊(C7⋊C8) | 2 |
| #11728263 | 2 |
| #11728255 | 2 |
| #11728245 | 2 |
| #11725517 | 2 |
| #10461 | 7 |