Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
558 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#89951 | C2 | semidirect |
| 3. C7×#1971 | C2 | semidirect |
| 4. C2×#89283 | C2 | semidirect |
| 5. #11725470 | C2 | semidirect |
| 28. C2×C7×Q16 | D4 | semidirect |
| 57. #6386 | D4 | semidirect |
| 62. #1971 | D7 | semidirect |
| 169. C2×Q16 | D28 | semidirect |
| 287. C7 | #13342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89951 | 2 |
| #11735944 | 2 |
| C7×#1971 | 2 |
| C2×#89283 | 2 |
| #11725470 | 2 |
| #13342 | 7 |