Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. M16×#595 | C2 | semidirect |
| 4. #11763688 | C2 | semidirect |
| 15. #10587553 | C4 | semidirect |
| 18. C17×#100 | C4 | semidirect |
| 19. #10587504 | C4 | semidirect |
| 20. #10587494 | C4 | semidirect |
| 35. #63247 | C2×C4 | semidirect |
| 41. M16×C17 | C2×C4 | semidirect |
| 42. #63223 | C2×C4 | semidirect |
| 87. #595 | #100 | direct (N × H) |
| 114. #100 | #595 | direct (N × H) |
| 117. C17 | C4×#100 | semidirect |
| 135. M16 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#595 | 2 |
| D17⋊#100 | 2 |
| M16×#595 | 2 |
| #11763688 | 2 |
| #100×D17 | 2 |
| C4×#100 | 17 |