Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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. #11727044 | C2 | semidirect |
| 3. #11725812 | C2 | semidirect |
| 4. C8×D56 | C2 | semidirect |
| 5. C7×#1367 | C2 | semidirect |
| 6. #11725371 | C2 | semidirect |
| 7. #11725366 | C2 | semidirect |
| 50. #1367 | D7 | semidirect |
| 74. D56 | SD16 | semidirect |
| 209. C7 | #12418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11727044 | 2 |
| #11727040 | 2 |
| #11725812 | 2 |
| C8×D56 | 2 |
| C7×#1367 | 2 |
| #11725371 | 2 |
| #11725366 | 2 |
| #12418 | 7 |