Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
306 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11726819 | C2 | semidirect |
| 2. #11726815 | C2 | semidirect |
| 4. #11726812 | C2 | semidirect |
| 5. #11725814 | C2 | semidirect |
| 6. #11725812 | C2 | semidirect |
| 7. C7×#1312 | C2 | semidirect |
| 53. #1312 | D7 | semidirect |
| 206. C7 | #12527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11726819 | 2 |
| #11726815 | 2 |
| #11726814 | 2 |
| #11726812 | 2 |
| #11725814 | 2 |
| #11725812 | 2 |
| C7×#1312 | 2 |
| #12527 | 7 |