Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
390 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11726847 | C2 | semidirect |
| 3. #11726538 | C2 | semidirect |
| 4. C7×#1347 | C2 | semidirect |
| 5. #11725580 | C2 | semidirect |
| 6. #11725332 | C2 | semidirect |
| 7. #11725291 | C2 | semidirect |
| 10. #89923 | C4 | semidirect |
| 11. D8×Dic7 | C4 | semidirect |
| 17. #89646 | C4 | semidirect |
| 18. #89644 | C4 | semidirect |
| 68. #1347 | D7 | semidirect |
| 315. C7 | #11744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11738142 | 2 |
| #11726847 | 2 |
| #11726538 | 2 |
| C7×#1347 | 2 |
| #11725580 | 2 |
| #11725332 | 2 |
| #11725291 | 2 |
| #11744 | 7 |