Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
612 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11734104 | C2 | semidirect |
| 2. C7×#2014 | C2 | semidirect |
| 3. #11729522 | C2 | semidirect |
| 5. #11725448 | C2 | semidirect |
| 6. #11725286 | C2 | semidirect |
| 7. #11725285 | C2 | semidirect |
| 70. #2014 | D7 | semidirect |
| 110. C2×D28 | SD16 | semidirect |
| 437. C7 | #7745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11734104 | 2 |
| C7×#2014 | 2 |
| #11729522 | 2 |
| #11729521 | 2 |
| #11725448 | 2 |
| #11725286 | 2 |
| #11725285 | 2 |
| #7745 | 7 |