Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
570 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 103 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. #11740661 | C2 | semidirect |
| 2. #11740658 | C2 | semidirect |
| 4. C7×#1993 | C2 | semidirect |
| 5. #11727299 | C2 | semidirect |
| 6. #11727299 | C2 | semidirect |
| 7. #11725467 | C2 | semidirect |
| 81. #1993 | D7 | semidirect |
| 111. C2×C7×C8 | SD16 | semidirect |
| 298. C2×C8 | #1143 | semidirect |
| 362. C7 | #10221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740661 | 2 |
| #11740658 | 2 |
| #11735944 | 2 |
| C7×#1993 | 2 |
| #11727299 | 2 |
| #11725467 | 2 |
| #10221 | 7 |