Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
632 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 632 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. #11730834 | C2 | semidirect |
| 3. #11728544 | C2 | semidirect |
| 4. #11728528 | C2 | semidirect |
| 5. #11727194 | C2 | semidirect |
| 6. C7×#1274 | C2 | semidirect |
| 7. #11725544 | C2 | semidirect |
| 21. #89467 | C4 | semidirect |
| 22. #89466 | C4 | semidirect |
| 48. #6437 | C2×C4 | semidirect |
| 54. #6432 | C2×C4 | semidirect |
| 60. C4×C7×C8 | C2×C4 | semidirect |
| 76. #1274 | D7 | semidirect |
| 114. C42×C7 | D8 | semidirect |
| 241. C4×C8 | C4×D7 | semidirect |
| 323. C42 | D56 | semidirect |
| 388. C7 | #9299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736748 | 2 |
| #11730834 | 2 |
| #11728544 | 2 |
| #11728528 | 2 |
| #11727194 | 2 |
| C7×#1274 | 2 |
| #11725544 | 2 |
| #9299 | 7 |