Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
640 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 1. C7×#3208 | C2 | semidirect |
| 2. #11740808 | C2 | semidirect |
| 4. #11729595 | C2 | semidirect |
| 5. #11729515 | C2 | semidirect |
| 6. #11728543 | C2 | semidirect |
| 7. #11725550 | C2 | semidirect |
| 80. #3208 | D7 | semidirect |
| 137. #1136 | SD16 | semidirect |
| 387. C7 | #10194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3208 | 2 |
| #11740808 | 2 |
| #11740608 | 2 |
| #11729595 | 2 |
| #11729515 | 2 |
| #11728543 | 2 |
| #11725550 | 2 |
| #10194 | 7 |