Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
398 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11736762 | C2 | semidirect |
| 4. #11728531 | C2 | semidirect |
| 6. C7×#1302 | C2 | semidirect |
| 7. #11725468 | C2 | semidirect |
| 73. #1302 | D7 | semidirect |
| 275. C7 | #9008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736762 | 2 |
| #11735942 | 2 |
| #11728555 | 2 |
| #11728531 | 2 |
| #11728519 | 2 |
| C7×#1302 | 2 |
| #11725468 | 2 |
| #9008 | 7 |