Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
474 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. C7×#1979 | C2 | semidirect |
| 4. C2×#89359 | C2 | semidirect |
| 6. #11725538 | C2 | semidirect |
| 7. #11725477 | C2 | semidirect |
| 17. #89951 | C4 | semidirect |
| 36. C2×C7×Q16 | C2×C4 | semidirect |
| 68. #6386 | C2×C4 | semidirect |
| 77. #1979 | D7 | semidirect |
| 198. C2×Q16 | C4×D7 | semidirect |
| 339. C7 | #13023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89951 | 2 |
| #11736007 | 2 |
| C7×#1979 | 2 |
| C2×#89359 | 2 |
| C2×#89292 | 2 |
| #11725538 | 2 |
| #11725477 | 2 |
| #13023 | 7 |