Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11729766 | C2 | semidirect |
| 4. #11725497 | C2 | semidirect |
| 5. C2×C7×#131 | C4 | semidirect |
| 10. C7×#423 | C4 | semidirect |
| 11. C7×#408 | C4 | semidirect |
| 13. C2×C7×#97 | C4 | semidirect |
| 91. C2×#131 | Dic7 | semidirect |
| 97. #423 | Dic7 | semidirect |
| 99. #408 | Dic7 | semidirect |
| 101. C2×#97 | Dic7 | semidirect |
| 250. C7 | #12808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2932 | 2 |
| #11729766 | 2 |
| #11729573 | 2 |
| #11725497 | 2 |
| #12808 | 7 |