Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
174 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 65 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. C4×D136 | C2 | semidirect |
| 3. #11762634 | C2 | semidirect |
| 4. #11762610 | C2 | semidirect |
| 5. #11762609 | C2 | semidirect |
| 6. C4×#63214 | C2 | semidirect |
| 7. C4×D8×C17 | C2 | semidirect |
| 15. #10587497 | C4 | direct (N × H) |
| 25. D8×C17 | C2×C4 | semidirect |
| 34. D136 | C2×C4 | semidirect |
| 36. #63214 | C2×C4 | semidirect |
| 63. C4×C17 | D16 | semidirect |
| 69. C4×D8 | D17 | semidirect |
| 91. C17 | C4×D16 | semidirect |
| 99. D8 | C4×D17 | semidirect |
| 135. C4 | #10587497 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587497 | 2 |
| C4×D136 | 2 |
| #11762634 | 2 |
| #11762610 | 2 |
| #11762609 | 2 |
| C4×#63214 | 2 |
| C4×D8×C17 | 2 |
| C4×D16 | 17 |