Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
578 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 3. C7×#2245 | C2 | semidirect |
| 4. #11729107 | C2 | semidirect |
| 5. #11729065 | C2 | semidirect |
| 7. #11726969 | C2 | semidirect |
| 8. #11726837 | C2 | semidirect |
| 77. #2245 | D7 | semidirect |
| 275. C7 | #33705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739361 | 2 |
| D7×#494 | 2 |
| C7×#2245 | 2 |
| #11729107 | 2 |
| #11729065 | 2 |
| #11726976 | 2 |
| #11726969 | 2 |
| #11726837 | 2 |
| #11726825 | 2 |
| #33705 | 7 |