Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
216 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 51 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. #11729218 | C2 | semidirect |
| 2. #11729212 | C2 | semidirect |
| 3. #11727127 | C2 | semidirect |
| 4. #11727111 | C2 | semidirect |
| 5. C7×#1419 | C2 | semidirect |
| 6. #11725405 | C2 | semidirect |
| 7. #11725389 | C2 | semidirect |
| 38. Dic56 | D4 | semidirect |
| 42. D112 | D4 | semidirect |
| 51. #1419 | D7 | semidirect |
| 183. C7 | #13692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11729218 | 2 |
| #11729212 | 2 |
| #11727127 | 2 |
| #11727111 | 2 |
| C7×#1419 | 2 |
| #11725405 | 2 |
| #11725389 | 2 |
| #13692 | 7 |