Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
690 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 95 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. #11736780 | C2 | semidirect |
| 3. C7×#1555 | C2 | semidirect |
| 4. #11729514 | C2 | semidirect |
| 5. #11728581 | C2 | semidirect |
| 6. #11725556 | C2 | semidirect |
| 7. #11725555 | C2 | semidirect |
| 60. C7×C4⋊C8 | D4 | semidirect |
| 71. C4⋊(C7⋊C8) | D4 | semidirect |
| 77. #1555 | D7 | semidirect |
| 243. C4⋊C8 | C22⋊D7 | semidirect |
| 403. C7 | #9457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740633 | 2 |
| #11736780 | 2 |
| C7×#1555 | 2 |
| #11729514 | 2 |
| #11728581 | 2 |
| #11725556 | 2 |
| #11725555 | 2 |
| #9457 | 7 |