Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
640 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11740765 | C2 | semidirect |
| 3. #11740614 | C2 | semidirect |
| 4. #11729565 | C2 | semidirect |
| 5. #11729515 | C2 | semidirect |
| 6. #11727622 | C2 | semidirect |
| 7. #11725474 | C2 | semidirect |
| 115. C7×M16 | SD16 | semidirect |
| 311. M16 | #1142 | 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×#3151 | 2 |
| #11740765 | 2 |
| #11740614 | 2 |
| #11729565 | 2 |
| #11729515 | 2 |
| #11727622 | 2 |
| #11725474 | 2 |
| #10194 | 7 |