Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
222 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 87 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×C16 | C2 | semidirect |
| 4. Q8⋊(C7⋊C16) | C2 | semidirect |
| 6. #11725361 | C2 | semidirect |
| 7. #11725305 | C2 | semidirect |
| 45. Q8×C16 | D7 | semidirect |
| 93. C7×Q8 | M32 | semidirect |
| 175. Q8 | #6372 | semidirect |
| 194. C7 | #12056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Q8×C16 | 2 |
| C8×#1143 | 2 |
| #11726809 | 2 |
| Q8⋊(C7⋊C16) | 2 |
| #11725362 | 2 |
| #11725361 | 2 |
| #11725305 | 2 |
| #12056 | 7 |