Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1240 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 501 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. #11763545 | C2 | direct (N × H) |
| 2. C2×#10587622 | C2 | semidirect |
| 3. C2×#10587621 | C2 | semidirect |
| 4. C2×C4×Dic34 | C2 | semidirect |
| 5. C2×D4×Dic17 | C2 | semidirect |
| 15. #10587622 | C22 | semidirect |
| 16. #10587621 | C22 | semidirect |
| 17. D4×Dic17 | C22 | semidirect |
| 21. C4×Dic34 | C22 | semidirect |
| 75. C2×C17 | #559 | semidirect |
| 93. C17 | C2×#559 | semidirect |
| 140. C2 | #11763545 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763545 | 2 |
| C2×#10587622 | 2 |
| C2×#10587621 | 2 |
| C2×C4×Dic34 | 2 |
| C2×D4×Dic17 | 2 |
| C2×C17×#127 | 2 |
| C2×#559 | 17 |