Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
338 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 73 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. #11728693 | C2 | semidirect |
| 4. #11726812 | C2 | semidirect |
| 5. C7×Q8⋊C16 | C2 | semidirect |
| 6. #11725370 | C2 | semidirect |
| 7. #11725310 | C2 | semidirect |
| 59. Q8⋊C16 | D7 | semidirect |
| 91. D56 | SD16 | semidirect |
| 114. C7×Q8 | D16 | semidirect |
| 228. Q8 | D112 | semidirect |
| 251. C7 | #12352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D56 | 2 |
| #11728693 | 2 |
| #11727040 | 2 |
| #11726812 | 2 |
| C7×Q8⋊C16 | 2 |
| #11725370 | 2 |
| #11725310 | 2 |
| #12352 | 7 |