Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
712 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 171 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. C22×C7×SD32 | C2 | semidirect |
| 2. #11741319 | C2 | semidirect |
| 3. C2×#89951 | C2 | semidirect |
| 5. #11729787 | C2 | semidirect |
| 6. #11729232 | C2 | semidirect |
| 7. #11729229 | C2 | semidirect |
| 8. #11729166 | C2 | semidirect |
| 9. #11729155 | C2 | semidirect |
| 21. Q16×Dic7 | C22 | semidirect |
| 22. C2×#6403 | C22 | semidirect |
| 24. C2×#6402 | C22 | semidirect |
| 32. #89304 | C22 | semidirect |
| 33. #89298 | C22 | semidirect |
| 34. Dic7⋊C16 | C22 | semidirect |
| 41. C2×C7×Q16 | D4 | semidirect |
| 79. C22×SD32 | D7 | semidirect |
| 200. C2×Q16 | C22⋊D7 | semidirect |
| 332. C7 | #33587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×SD32 | 2 |
| #11741319 | 2 |
| C2×#89951 | 2 |
| #11741275 | 2 |
| #11729787 | 2 |
| #11729232 | 2 |
| #11729229 | 2 |
| #11729166 | 2 |
| #11729155 | 2 |
| #33587 | 7 |