Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
302 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 63 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. #11736975 | C2 | semidirect |
| 3. #11727046 | C2 | semidirect |
| 4. #11726834 | C2 | semidirect |
| 5. C7×#1330 | C2 | semidirect |
| 6. #11725369 | C2 | semidirect |
| 7. #11725323 | C2 | semidirect |
| 68. #1330 | D7 | semidirect |
| 271. C7 | #12349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736975 | 2 |
| #11728622 | 2 |
| #11727046 | 2 |
| #11726834 | 2 |
| C7×#1330 | 2 |
| #11725369 | 2 |
| #11725323 | 2 |
| #12349 | 7 |