Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
588 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 588 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 |
|---|---|---|
| 2. #11731062 | C2 | semidirect |
| 3. C7×#1502 | C2 | semidirect |
| 4. #11729569 | C2 | semidirect |
| 5. #11728516 | C2 | semidirect |
| 6. #11725542 | C2 | semidirect |
| 7. #11725426 | C2 | semidirect |
| 15. #89859 | C4 | semidirect |
| 16. #89844 | C4 | semidirect |
| 78. #1502 | D7 | semidirect |
| 134. C4×Dic7 | D8 | semidirect |
| 399. C7 | #9237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740743 | 2 |
| #11731062 | 2 |
| C7×#1502 | 2 |
| #11729569 | 2 |
| #11728516 | 2 |
| #11725542 | 2 |
| #11725426 | 2 |
| #9237 | 7 |