Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1306 conjugacy classes of subgroups; only the 279 normal subgroups are shown.
This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 279 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×#3573 | C2 | semidirect |
| 3. #11741240 | C2 | semidirect |
| 4. #11729899 | C2 | semidirect |
| 5. #11729783 | C2 | semidirect |
| 6. #11729780 | C2 | semidirect |
| 7. #11729765 | C2 | semidirect |
| 14. C22×#1131 | C22 | semidirect |
| 21. #89898 | C22 | semidirect |
| 22. #89891 | C22 | semidirect |
| 24. #89873 | C22 | semidirect |
| 25. #89351 | C22 | semidirect |
| 40. C2×C7×M16 | D4 | semidirect |
| 43. C22×C7×C8 | D4 | semidirect |
| 63. #3573 | D7 | semidirect |
| 169. C2×M16 | C22⋊D7 | semidirect |
| 173. C22×C8 | C22⋊D7 | semidirect |
| 271. C7 | #21484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3573 | 2 |
| #11741570 | 2 |
| #11741240 | 2 |
| #11729899 | 2 |
| #11729783 | 2 |
| #11729780 | 2 |
| #11729765 | 2 |
| #21484 | 7 |