Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
924 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 210 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. C2×D4×#595 | C2 | semidirect |
| 2. #11763761 | C2 | semidirect |
| 3. #11763755 | C2 | semidirect |
| 4. C42×#595 | C2 | semidirect |
| 13. C17×#127 | C4 | semidirect |
| 14. #10587626 | C4 | semidirect |
| 15. #10587560 | C4 | semidirect |
| 22. C2×D4×C17 | C2×C4 | semidirect |
| 23. C2×C22⋊D17 | C2×C4 | semidirect |
| 26. C2×D68 | C2×C4 | semidirect |
| 31. C4×#595 | D4 | semidirect |
| 32. C42×C17 | C2×C4 | semidirect |
| 33. C4×Dic17 | C2×C4 | semidirect |
| 61. #595 | #127 | direct (N × H) |
| 62. C4×C17 | C4×D4 | semidirect |
| 63. Dic17 | C4×D4 | semidirect |
| 78. #127 | #595 | direct (N × H) |
| 85. C17 | C4×#127 | semidirect |
| 91. C2×D4 | C2×#595 | semidirect |
| 102. C42 | C2×#595 | semidirect |
| 131. C4 | D4×#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 |
| #11763761 | 2 |
| #11763755 | 2 |
| C42×#595 | 2 |
| #127×D17 | 2 |
| C4×#127 | 17 |