Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
814 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#89687 | C2 | semidirect |
| 2. D7×#494 | C2 | semidirect |
| 4. C7×#2248 | C2 | semidirect |
| 5. #11729236 | C2 | semidirect |
| 6. #11729066 | C2 | semidirect |
| 7. #11729045 | C2 | semidirect |
| 8. #11726820 | C2 | semidirect |
| 9. C4×#6372 | C2 | semidirect |
| 78. #6372 | D4 | semidirect |
| 84. #2248 | D7 | semidirect |
| 234. C4×C7 | #510 | semidirect |
| 317. C7 | #33718 | semidirect |
| 328. C4 | #89687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89687 | 2 |
| D7×#494 | 2 |
| #11739227 | 2 |
| C7×#2248 | 2 |
| #11729236 | 2 |
| #11729066 | 2 |
| #11729045 | 2 |
| #11726820 | 2 |
| C4×#6372 | 2 |
| #33718 | 7 |