Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
536 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 101 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×#3156 | C2 | semidirect |
| 3. C2×#89951 | C2 | semidirect |
| 4. #11729830 | C2 | semidirect |
| 5. #11729815 | C2 | semidirect |
| 6. #11727651 | C2 | semidirect |
| 7. #11725478 | C2 | semidirect |
| 89. #3156 | D7 | semidirect |
| 399. C7 | #13335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3156 | 2 |
| #11741339 | 2 |
| C2×#89951 | 2 |
| #11729830 | 2 |
| #11729815 | 2 |
| #11727651 | 2 |
| #11725478 | 2 |
| #13335 | 7 |