Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
924 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 289 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×Dic17 | C2 | semidirect |
| 2. #11762712 | C2 | semidirect |
| 3. #11762679 | C2 | semidirect |
| 4. C42×Dic17 | C2 | semidirect |
| 8. C17×#127 | C4 | semidirect |
| 18. C2×D4×C17 | C2×C4 | semidirect |
| 24. C42×C17 | C2×C4 | semidirect |
| 28. C4×Dic17 | D4 | semidirect |
| 49. C4×C17 | C4×D4 | semidirect |
| 52. Dic17 | #127 | direct (N × H) |
| 64. #127 | Dic17 | direct (N × H) |
| 71. C17 | C4×#127 | semidirect |
| 75. C2×D4 | C2×Dic17 | semidirect |
| 85. C42 | C2×Dic17 | semidirect |
| 108. C4 | D4×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic17 | 2 |
| #11762712 | 2 |
| #11762679 | 2 |
| C42×Dic17 | 2 |
| C2×C17×#127 | 2 |
| C4×#127 | 17 |