Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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×#2155 | C2 | semidirect |
| 5. #11728439 | C2 | semidirect |
| 6. #11725628 | C2 | semidirect |
| 7. #11725533 | C2 | semidirect |
| 22. #89309 | C4 | semidirect |
| 45. C7×M32 | C2×C4 | semidirect |
| 57. #6386 | C2×C4 | semidirect |
| 63. #2155 | D7 | semidirect |
| 174. M32 | C4×D7 | semidirect |
| 276. C7 | #12932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736622 | 2 |
| C7×#2155 | 2 |
| C2×#89309 | 2 |
| #11728466 | 2 |
| #11728439 | 2 |
| #11725628 | 2 |
| #11725533 | 2 |
| #12932 | 7 |