Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
558 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 199 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 |
|---|---|---|
| 2. C7×#2254 | C2 | semidirect |
| 3. #11729139 | C2 | semidirect |
| 5. #11727094 | C2 | semidirect |
| 7. #11726800 | C2 | semidirect |
| 48. D7×C16 | Q8 | semidirect |
| 53. #2254 | D7 | direct (N × H) |
| 78. C7×C16 | C2×Q8 | semidirect |
| 79. C7⋊C16 | C2×Q8 | semidirect |
| 171. C16 | Q8×D7 | semidirect |
| 174. D7 | #2254 | direct (N × H) |
| 193. C7 | C2×#2254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×#500 | 2 |
| C7×#2254 | 2 |
| #11729139 | 2 |
| D7×#367 | 2 |
| #11727094 | 2 |
| C4×D7×C16 | 2 |
| #11726800 | 2 |
| C2×#2254 | 7 |