Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1022 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 199 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. C2×D7×D16 | C2 | semidirect |
| 2. D7×#493 | C2 | semidirect |
| 3. C7×#2246 | C2 | semidirect |
| 4. #11729218 | C2 | semidirect |
| 5. #11729044 | C2 | semidirect |
| 6. #11726814 | C2 | semidirect |
| 7. C4×D7×C16 | C2 | semidirect |
| 11. C2×C7×D16 | C22 | semidirect |
| 12. C7×#493 | C22 | semidirect |
| 14. #89923 | C22 | semidirect |
| 15. C2×#6400 | C22 | semidirect |
| 18. C2×D112 | C22 | semidirect |
| 20. #89467 | C22 | semidirect |
| 22. C4×C7×C16 | C22 | semidirect |
| 23. C16×Dic7 | C22 | semidirect |
| 24. C4×C7⋊C16 | C22 | semidirect |
| 52. D7×C16 | D4 | semidirect |
| 58. #2246 | D7 | direct (N × H) |
| 87. C7×C16 | C2×D4 | semidirect |
| 88. C7⋊C16 | C2×D4 | semidirect |
| 95. C2×D16 | C2×D7 | semidirect |
| 101. #493 | C2×D7 | semidirect |
| 105. C4×C16 | C2×D7 | semidirect |
| 123. C4×D7 | D16 | semidirect |
| 165. C4×C7 | C2×D16 | semidirect |
| 169. Dic7 | C2×D16 | semidirect |
| 198. C16 | D4×D7 | semidirect |
| 203. D7 | #2246 | direct (N × H) |
| 228. C7 | C2×#2246 | semidirect |
| 239. C4 | D7×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×D16 | 2 |
| D7×#493 | 2 |
| C7×#2246 | 2 |
| #11729218 | 2 |
| #11729044 | 2 |
| #11726814 | 2 |
| C4×D7×C16 | 2 |
| C2×#2246 | 7 |