Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1008 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 285 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 |
|---|---|---|
| 2. C22×#63223 | C2 | semidirect |
| 3. #11762772 | C2 | direct (N × H) |
| 4. C2×#10587491 | C2 | semidirect |
| 5. C22×M16×C17 | C2 | semidirect |
| 16. C2×M16×C17 | C22 | semidirect |
| 17. C22×C8×C17 | C22 | semidirect |
| 19. C2×#63223 | C22 | semidirect |
| 20. C22×#3622 | C22 | semidirect |
| 21. #10587491 | C22 | semidirect |
| 47. C2×C8×C17 | C23 | semidirect |
| 50. C2×#3622 | C23 | semidirect |
| 60. C22×D17 | M16 | semidirect |
| 91. C2×D17 | C2×M16 | semidirect |
| 99. C22×M16 | D17 | semidirect |
| 103. C2×C17 | #407 | semidirect |
| 119. C2×M16 | C2×D17 | semidirect |
| 121. C22×C8 | C2×D17 | semidirect |
| 123. C17 | C2×#407 | semidirect |
| 152. C2×C8 | C22×D17 | semidirect |
| 200. C2 | #11762772 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D17 | 2 |
| C22×#63223 | 2 |
| #11762772 | 2 |
| C2×#10587491 | 2 |
| C22×M16×C17 | 2 |
| C2×#407 | 17 |