Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
564 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 173 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×#63229 | C2 | semidirect |
| 2. C23×#3622 | C2 | semidirect |
| 3. C2×#10587610 | C2 | semidirect |
| 4. #11763036 | C2 | direct (N × H) |
| 5. C2×#10587479 | C2 | semidirect |
| 6. C2×#10587481 | C2 | semidirect |
| 7. C2×#10587503 | C2 | semidirect |
| 19. C2×#63229 | C22 | semidirect |
| 22. #10587610 | C22 | semidirect |
| 27. C22×#3622 | C22 | semidirect |
| 28. #10587503 | C22 | semidirect |
| 29. #10587481 | C22 | semidirect |
| 30. #10587479 | C22 | semidirect |
| 62. C2×#3622 | D4 | semidirect |
| 71. C23×C17 | SD16 | semidirect |
| 97. #3622 | C2×D4 | semidirect |
| 108. C22×C17 | C2×SD16 | semidirect |
| 128. C2×C17 | #465 | semidirect |
| 154. C17 | C2×#465 | semidirect |
| 195. C23 | #63229 | semidirect |
| 230. C22 | C2×#63229 | semidirect |
| 243. C2 | #11763036 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63229 | 2 |
| C23×#3622 | 2 |
| C2×#10587610 | 2 |
| #11763036 | 2 |
| C2×#10587479 | 2 |
| C2×#10587481 | 2 |
| C2×#10587503 | 2 |
| C2×C17×#121 | 2 |
| C2×#465 | 17 |