Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
424 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 69 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. #11729042 | C2 | semidirect |
| 3. #11727043 | C2 | semidirect |
| 4. #11726332 | C2 | semidirect |
| 5. C7×#1361 | C2 | semidirect |
| 6. #11725362 | C2 | semidirect |
| 7. #11725277 | C2 | semidirect |
| 17. #89454 | C22 | semidirect |
| 18. C7×C4⋊C16 | C22 | semidirect |
| 19. C7×#335 | C22 | semidirect |
| 24. C4×C7⋊C16 | C22 | semidirect |
| 59. #1361 | D7 | semidirect |
| 94. D56 | SD16 | semidirect |
| 111. C4⋊C16 | C2×D7 | semidirect |
| 115. #335 | C2×D7 | semidirect |
| 277. C7 | #12368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739234 | 2 |
| #11729042 | 2 |
| #11727043 | 2 |
| #11726332 | 2 |
| C7×#1361 | 2 |
| #11725362 | 2 |
| #11725277 | 2 |
| #12368 | 7 |