Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
514 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 93 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. #11735931 | C2 | semidirect |
| 3. #11728517 | C2 | semidirect |
| 4. #11728515 | C2 | semidirect |
| 5. #11727552 | C2 | semidirect |
| 6. C7×#1302 | C2 | semidirect |
| 7. #11725559 | C2 | semidirect |
| 89. #1302 | D7 | semidirect |
| 373. C7 | #9311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736792 | 2 |
| #11735931 | 2 |
| #11728517 | 2 |
| #11728515 | 2 |
| #11727552 | 2 |
| C7×#1302 | 2 |
| #11725559 | 2 |
| #9311 | 7 |