Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1258 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 1258 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. #11740762 | C2 | semidirect |
| 3. #11739829 | C2 | semidirect |
| 4. #11729600 | C2 | semidirect |
| 5. #11729565 | C2 | semidirect |
| 6. #11729355 | C2 | semidirect |
| 16. C2×#6432 | C22 | semidirect |
| 21. #89812 | C22 | semidirect |
| 24. #89719 | C22 | semidirect |
| 25. C4×C4⋊Dic7 | C22 | semidirect |
| 26. #89697 | C22 | semidirect |
| 27. #89332 | C22 | semidirect |
| 28. #89320 | C22 | semidirect |
| 98. C2×C7×D4 | SD16 | semidirect |
| 280. C2×D4 | #1142 | semidirect |
| 359. C7 | #18388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3496 | 2 |
| #11740762 | 2 |
| #11739829 | 2 |
| #11729600 | 2 |
| #11729565 | 2 |
| #11729355 | 2 |
| #18388 | 7 |