Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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. #11726812 | C2 | semidirect |
| 2. C16×D28 | C2 | semidirect |
| 3. #11726333 | C2 | semidirect |
| 5. C7×#1372 | C2 | semidirect |
| 6. #11725282 | C2 | semidirect |
| 7. #11725279 | C2 | semidirect |
| 49. #1372 | D7 | semidirect |
| 203. C7 | #12468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11726812 | 2 |
| C16×D28 | 2 |
| #11726333 | 2 |
| #11726330 | 2 |
| C7×#1372 | 2 |
| #11725282 | 2 |
| #11725279 | 2 |
| #12468 | 7 |