Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. C7×#2956 | C2 | semidirect |
| 2. #11735980 | C2 | semidirect |
| 3. #11729866 | C2 | semidirect |
| 4. #11728683 | C2 | semidirect |
| 5. #11728680 | C2 | semidirect |
| 6. #11728673 | C2 | semidirect |
| 7. #11728477 | C2 | semidirect |
| 8. #11727618 | C2 | semidirect |
| 23. #89483 | C22 | semidirect |
| 24. #89467 | C22 | semidirect |
| 26. #89452 | C22 | semidirect |
| 29. #89290 | C22 | semidirect |
| 30. #89289 | C22 | semidirect |
| 31. #89261 | C22 | semidirect |
| 32. #89258 | C22 | semidirect |
| 73. #2956 | D7 | semidirect |
| 98. C7×Q16 | #41 | semidirect |
| 102. C7×D8 | #41 | semidirect |
| 253. Q16 | #1157 | semidirect |
| 259. D8 | #1157 | semidirect |
| 318. C7 | #33688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2956 | 2 |
| #11735980 | 2 |
| #11729866 | 2 |
| #11728683 | 2 |
| #11728680 | 2 |
| #11728673 | 2 |
| #11728477 | 2 |
| #11727618 | 2 |
| #33688 | 7 |