Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
786 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 187 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. C22×D112 | C2 | semidirect |
| 2. C22×#6372 | C2 | semidirect |
| 3. C2×#89655 | C2 | semidirect |
| 4. C2×C7×#367 | C2 | semidirect |
| 5. C2×#89286 | C2 | semidirect |
| 6. #11727102 | C2 | direct (N × H) |
| 15. C2×D112 | C22 | semidirect |
| 17. C2×#6372 | C22 | semidirect |
| 19. #89655 | C22 | semidirect |
| 20. C7×#367 | C22 | semidirect |
| 21. #89286 | C22 | semidirect |
| 40. C2×C7×C16 | D4 | semidirect |
| 53. C2×#367 | D7 | semidirect |
| 85. C7×C16 | C2×D4 | semidirect |
| 100. #367 | C2×D7 | semidirect |
| 150. C2×C16 | D28 | semidirect |
| 201. C16 | C2×D28 | semidirect |
| 202. C2×C7 | #2218 | semidirect |
| 234. C7 | C2×#2218 | semidirect |
| 252. C2 | #11727102 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D112 | 2 |
| C22×#6372 | 2 |
| C2×#89655 | 2 |
| C2×C7×#367 | 2 |
| C2×#89286 | 2 |
| #11727102 | 2 |
| C2×#2218 | 7 |