Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 97 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×#3060 | C2 | semidirect |
| 2. #11741339 | C2 | semidirect |
| 3. #11741250 | C2 | semidirect |
| 4. #11729834 | C2 | semidirect |
| 5. #11729760 | C2 | semidirect |
| 6. C2×#89283 | C2 | semidirect |
| 7. #11725526 | C2 | semidirect |
| 64. C2×Dic28 | D4 | semidirect |
| 69. C2×D56 | D4 | semidirect |
| 82. #6393 | D4 | semidirect |
| 88. C2×C7⋊C16 | D4 | semidirect |
| 91. #3060 | D7 | semidirect |
| 426. C7 | #13318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3060 | 2 |
| #11741339 | 2 |
| #11741250 | 2 |
| #11729834 | 2 |
| #11729760 | 2 |
| C2×#89283 | 2 |
| #11725526 | 2 |
| #13318 | 7 |