Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
304 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 304 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×Dic28 | C2 | semidirect |
| 5. C7×Q8⋊C16 | C2 | semidirect |
| 6. #11725371 | C2 | semidirect |
| 7. #11725311 | C2 | semidirect |
| 59. Q8⋊C16 | D7 | semidirect |
| 86. Dic28 | SD16 | semidirect |
| 111. C7×Q8 | SD32 | semidirect |
| 217. Q8 | #6374 | semidirect |
| 236. C7 | #12354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic28 | 2 |
| #11728693 | 2 |
| #11727046 | 2 |
| #11726812 | 2 |
| C7×Q8⋊C16 | 2 |
| #11725371 | 2 |
| #11725311 | 2 |
| #12354 | 7 |