Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
840 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#89331 | C2 | semidirect |
| 3. #11729373 | C2 | semidirect |
| 4. C4×#6407 | C2 | semidirect |
| 5. C23×C7×D4 | C4 | semidirect |
| 12. C7×#380 | C4 | semidirect |
| 13. C7×#379 | C4 | semidirect |
| 52. #6407 | D4 | semidirect |
| 114. C23×D4 | Dic7 | semidirect |
| 125. #380 | Dic7 | semidirect |
| 126. #379 | Dic7 | semidirect |
| 251. C4×C7 | AΣL(1,𝔽16) | semidirect |
| 371. C7 | #13218 | semidirect |
| 405. C4 | #89331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2408 | 2 |
| C2×#89331 | 2 |
| #11729373 | 2 |
| C4×#6407 | 2 |
| #13218 | 7 |