Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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. C7×Q8×Q16 | C2 | semidirect |
| 5. #11725608 | C2 | semidirect |
| 6. Q8⋊(C7⋊C16) | C2 | semidirect |
| 7. #11725571 | C2 | semidirect |
| 54. Q8×Q16 | D7 | semidirect |
| 69. C7×Q16 | SD16 | semidirect |
| 115. C7×Q8 | SD32 | semidirect |
| 184. Q16 | #1143 | semidirect |
| 217. Q8 | #6402 | semidirect |
| 236. C7 | #12354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Q8×Q16 | 2 |
| #11729135 | 2 |
| #11728693 | 2 |
| #11728668 | 2 |
| #11725608 | 2 |
| Q8⋊(C7⋊C16) | 2 |
| #11725571 | 2 |
| #12354 | 7 |