Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
458 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 71 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×#2126 | C2 | semidirect |
| 3. #11729573 | C2 | semidirect |
| 4. #11725347 | C2 | semidirect |
| 8. C2×#6437 | C4 | semidirect |
| 11. #89857 | C4 | semidirect |
| 15. C4×#1136 | C4 | semidirect |
| 17. C7×#353 | C22 | semidirect |
| 18. #89340 | C22 | semidirect |
| 54. #2126 | D7 | semidirect |
| 114. #353 | C2×D7 | semidirect |
| 288. C7 | #13585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740732 | 2 |
| C7×#2126 | 2 |
| #11729573 | 2 |
| #11725347 | 2 |
| #13585 | 7 |