Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1254 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 1254 conjugacy classes of subgroups — too many to draw. Only its 207 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. #11740715 | C2 | semidirect |
| 3. #11739827 | C2 | semidirect |
| 4. #11729597 | C2 | semidirect |
| 5. #11729565 | C2 | semidirect |
| 6. #11729355 | C2 | semidirect |
| 17. C2×#6432 | C22 | semidirect |
| 21. #89805 | C22 | semidirect |
| 24. #89725 | C22 | semidirect |
| 25. C4×C4⋊Dic7 | C22 | semidirect |
| 26. #89697 | C22 | semidirect |
| 27. #89332 | C22 | semidirect |
| 28. #89320 | C22 | semidirect |
| 363. C7 | #18394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3496 | 2 |
| #11740715 | 2 |
| #11739827 | 2 |
| #11729597 | 2 |
| #11729565 | 2 |
| #11729355 | 2 |
| #18394 | 7 |