Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 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. #11730836 | C2 | semidirect |
| 4. #11728533 | C2 | semidirect |
| 6. C7×#1274 | C2 | semidirect |
| 7. #11725544 | C2 | semidirect |
| 21. #89465 | C4 | semidirect |
| 22. #89453 | C4 | semidirect |
| 74. #1274 | D7 | semidirect |
| 100. C42×C7 | SD16 | semidirect |
| 284. C42 | #1132 | semidirect |
| 337. C7 | #9301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736757 | 2 |
| #11730836 | 2 |
| #11728544 | 2 |
| #11728533 | 2 |
| #11727194 | 2 |
| C7×#1274 | 2 |
| #11725544 | 2 |
| #9301 | 7 |