Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
650 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 111 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×#2275 | C2 | semidirect |
| 3. #11729353 | C2 | semidirect |
| 4. #11727246 | C2 | semidirect |
| 5. #11727186 | C2 | semidirect |
| 6. #11725427 | C2 | semidirect |
| 7. #11725421 | C2 | semidirect |
| 18. #89787 | C4 | semidirect |
| 20. #89780 | C4 | semidirect |
| 52. #6437 | C2×C4 | semidirect |
| 55. #6432 | C2×C4 | semidirect |
| 68. C4⋊(C7⋊C8) | C2×C4 | semidirect |
| 74. #2275 | D7 | semidirect |
| 158. C7×D4 | #104 | semidirect |
| 331. D4 | #6379 | semidirect |
| 361. C7 | #9325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2275 | 2 |
| #11739755 | 2 |
| #11729353 | 2 |
| #11727246 | 2 |
| #11727186 | 2 |
| #11725427 | 2 |
| #11725421 | 2 |
| #9325 | 7 |