Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
534 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 534 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×#3141 | C2 | semidirect |
| 3. #11740708 | C2 | semidirect |
| 4. #11729566 | C2 | semidirect |
| 5. #11729530 | C2 | semidirect |
| 6. #11727614 | C2 | semidirect |
| 7. #11725471 | C2 | semidirect |
| 77. #3141 | D7 | semidirect |
| 347. C7 | #10092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3141 | 2 |
| #11740751 | 2 |
| #11740708 | 2 |
| #11729566 | 2 |
| #11729530 | 2 |
| #11727614 | 2 |
| #11725471 | 2 |
| #10092 | 7 |