Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
586 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×C7×D16 | C2 | semidirect |
| 2. #11741275 | C2 | semidirect |
| 3. C2×#89919 | C2 | semidirect |
| 4. #11729795 | C2 | semidirect |
| 5. C2×#89358 | C2 | semidirect |
| 6. C2×#89305 | C2 | semidirect |
| 7. #11725611 | C2 | semidirect |
| 46. C2×C7×D8 | D4 | semidirect |
| 69. C2×C7×C16 | D4 | semidirect |
| 79. #6386 | D4 | semidirect |
| 82. C22×D16 | D7 | semidirect |
| 235. C2×D8 | C22⋊D7 | semidirect |
| 252. C2×C16 | C22⋊D7 | semidirect |
| 385. C7 | #13336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D16 | 2 |
| #11741275 | 2 |
| C2×#89919 | 2 |
| #11729795 | 2 |
| C2×#89358 | 2 |
| C2×#89305 | 2 |
| #11725611 | 2 |
| #13336 | 7 |