Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
542 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 99 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. #11740785 | C2 | semidirect |
| 4. C7×#1518 | C2 | semidirect |
| 6. #11727300 | C2 | semidirect |
| 7. #11725547 | C2 | semidirect |
| 82. #1518 | D7 | semidirect |
| 129. C2×C7⋊C8 | SD16 | semidirect |
| 345. C7 | #10220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740800 | 2 |
| #11740785 | 2 |
| #11736750 | 2 |
| C7×#1518 | 2 |
| #11727307 | 2 |
| #11727300 | 2 |
| #11725547 | 2 |
| #10220 | 7 |