Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
366 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 83 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. C7×#1546 | C2 | semidirect |
| 3. #11729544 | C2 | semidirect |
| 5. #11728507 | C2 | semidirect |
| 7. #11725516 | C2 | semidirect |
| 68. #1546 | D7 | semidirect |
| 288. C7 | #10491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740661 | 2 |
| C7×#1546 | 2 |
| #11729544 | 2 |
| #11728515 | 2 |
| #11728507 | 2 |
| #11728259 | 2 |
| #11725516 | 2 |
| #10491 | 7 |