Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
770 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 85 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. C7×#3213 | C2 | semidirect |
| 2. #11740732 | C2 | semidirect |
| 3. #11740424 | C2 | semidirect |
| 4. #11729566 | C2 | semidirect |
| 5. #11729472 | C2 | semidirect |
| 6. #11728572 | C2 | semidirect |
| 7. #11725554 | C2 | semidirect |
| 41. C7×C4⋊Q8 | D4 | semidirect |
| 42. C7×#127 | D4 | semidirect |
| 67. C7×C4⋊C8 | D4 | semidirect |
| 77. #6377 | D4 | semidirect |
| 79. #3213 | D7 | semidirect |
| 223. C4⋊Q8 | C22⋊D7 | semidirect |
| 229. #127 | C22⋊D7 | semidirect |
| 246. C4⋊C8 | C22⋊D7 | semidirect |
| 390. C7 | #10088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3213 | 2 |
| #11740732 | 2 |
| #11740424 | 2 |
| #11729566 | 2 |
| #11729472 | 2 |
| #11728572 | 2 |
| #11725554 | 2 |
| #10088 | 7 |