Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #11762849 | C2 | semidirect |
| 4. #11762848 | C2 | semidirect |
| 5. #11762847 | C2 | semidirect |
| 6. #11762844 | C2 | semidirect |
| 7. #106×D17 | C2 | semidirect |
| 8. C2×C17×#106 | C2 | semidirect |
| 15. #10587587 | C4 | semidirect |
| 38. C2×C8×C17 | C2×C4 | semidirect |
| 50. #63223 | C2×C4 | semidirect |
| 52. #63218 | C2×C4 | semidirect |
| 53. C8×D17 | C2×C4 | semidirect |
| 94. C2×#106 | D17 | semidirect |
| 119. C17 | #2912 | semidirect |
| 133. C2×C8 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587587 | 2 |
| #11763290 | 2 |
| #11762849 | 2 |
| #11762848 | 2 |
| #11762847 | 2 |
| #11762844 | 2 |
| #106×D17 | 2 |
| C2×C17×#106 | 2 |
| #2912 | 17 |