Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
424 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C7×#1952 | C2 | semidirect |
| 5. #11728350 | C2 | semidirect |
| 6. #11725535 | C2 | semidirect |
| 7. #11725477 | C2 | semidirect |
| 22. #89290 | C4 | semidirect |
| 46. C7×#108 | C2×C4 | semidirect |
| 59. #6386 | C2×C4 | semidirect |
| 68. #1952 | D7 | semidirect |
| 185. #108 | C4×D7 | semidirect |
| 293. C7 | #12940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736006 | 2 |
| C7×#1952 | 2 |
| C2×#89290 | 2 |
| C2×#89286 | 2 |
| #11728350 | 2 |
| #11725535 | 2 |
| #11725477 | 2 |
| #12940 | 7 |