Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
562 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 165 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. Q8×D56 | C2 | semidirect |
| 2. #11737355 | C2 | semidirect |
| 3. C7×Q8×C16 | C2 | semidirect |
| 4. #11727043 | C2 | semidirect |
| 5. #11727040 | C2 | semidirect |
| 6. #11726812 | C2 | semidirect |
| 7. C4×D112 | C2 | semidirect |
| 52. Q8×C16 | D7 | semidirect |
| 77. D56 | #41 | semidirect |
| 98. C7×Q8 | D16 | semidirect |
| 185. Q8 | D112 | semidirect |
| 202. C7 | #33925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D56 | 2 |
| #11737355 | 2 |
| C7×Q8×C16 | 2 |
| #11727043 | 2 |
| #11727040 | 2 |
| #11726812 | 2 |
| C4×D112 | 2 |
| #33925 | 7 |