Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
220 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11725810 | C2 | semidirect |
| 4. C7×#1311 | C2 | semidirect |
| 5. #11725311 | C2 | semidirect |
| 7. #11725306 | C2 | semidirect |
| 51. #1311 | D7 | semidirect |
| 75. C7×C16 | M16 | semidirect |
| 168. C16 | #1131 | semidirect |
| 194. C7 | #12084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6374 | 2 |
| #11725810 | 2 |
| #11725806 | 2 |
| C7×#1311 | 2 |
| #11725311 | 2 |
| #11725310 | 2 |
| #11725306 | 2 |
| #12084 | 7 |