Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
594 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. C7×#1518 | C2 | semidirect |
| 4. #11729594 | C2 | semidirect |
| 6. #11725543 | C2 | semidirect |
| 7. #11725437 | C2 | semidirect |
| 13. #89860 | C4 | semidirect |
| 14. #89857 | C4 | semidirect |
| 32. C7×C4⋊Q8 | C2×C4 | semidirect |
| 33. C7×C4⋊Q8 | C2×C4 | semidirect |
| 67. C4×C7⋊C8 | C2×C4 | semidirect |
| 72. #1518 | D7 | semidirect |
| 121. C4×Dic7 | SD16 | semidirect |
| 196. C4⋊Q8 | C4×D7 | semidirect |
| 197. C4⋊Q8 | C4×D7 | semidirect |
| 357. C7 | #9295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740800 | 2 |
| #11731598 | 2 |
| C7×#1518 | 2 |
| #11729594 | 2 |
| #11728528 | 2 |
| #11725543 | 2 |
| #11725437 | 2 |
| #9295 | 7 |