Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
162 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 50 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. Q16×#595 | C2 | semidirect |
| 3. #11763736 | C2 | semidirect |
| 4. #11763722 | C2 | semidirect |
| 6. C16×#595 | C2 | semidirect |
| 18. C17×SD32 | C4 | semidirect |
| 19. #10587499 | C4 | semidirect |
| 20. #10587498 | C4 | semidirect |
| 21. #10587471 | C4 | semidirect |
| 33. Q16×C17 | C2×C4 | semidirect |
| 37. Dic68 | C2×C4 | semidirect |
| 41. C16×C17 | C2×C4 | semidirect |
| 42. #63214 | C2×C4 | semidirect |
| 69. #595 | SD32 | direct (N × H) |
| 93. SD32 | #595 | direct (N × H) |
| 101. C17 | C4×SD32 | semidirect |
| 107. Q16 | C2×#595 | semidirect |
| 121. C16 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#595 | 2 |
| D8×#595 | 2 |
| #11763736 | 2 |
| #11763722 | 2 |
| #11763721 | 2 |
| C16×#595 | 2 |
| SD32×D17 | 2 |
| C4×SD32 | 17 |