Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 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. #11736697 | C2 | semidirect |
| 3. C2×C7×#359 | C2 | semidirect |
| 4. #11729834 | C2 | semidirect |
| 5. C2×#89303 | C2 | semidirect |
| 6. #11725614 | C2 | semidirect |
| 7. #11725539 | C2 | semidirect |
| 74. C2×#359 | D7 | semidirect |
| 336. C7 | #12995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741373 | 2 |
| #11736697 | 2 |
| C2×C7×#359 | 2 |
| #11729834 | 2 |
| C2×#89303 | 2 |
| #11725614 | 2 |
| #11725539 | 2 |
| #12995 | 7 |