Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. C2×Dic136 | C2 | semidirect |
| 3. C2×#10587500 | C2 | semidirect |
| 4. Q32×D17 | C2 | direct (N × H) |
| 6. C2×C17×Q32 | C2 | semidirect |
| 14. C17×Q32 | C22 | semidirect |
| 16. #10587500 | C22 | semidirect |
| 18. Dic136 | C22 | semidirect |
| 56. C2×D17 | Q32 | direct (N × H) |
| 67. C2×Q32 | D17 | direct (N × H) |
| 69. C2×C17 | C2×Q32 | semidirect |
| 71. D17 | C2×Q32 | direct (N × H) |
| 81. Q32 | C2×D17 | direct (N × H) |
| 85. C17 | C22×Q32 | semidirect |
| 129. C2 | Q32×D17 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D17 | 2 |
| C2×Dic136 | 2 |
| C2×#10587500 | 2 |
| Q32×D17 | 2 |
| C2×C16×D17 | 2 |
| C2×C17×Q32 | 2 |
| C22×Q32 | 17 |