Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
656 conjugacy classes of subgroups; only the 322 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 322 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×#63243 | C2 | direct (N × H) |
| 3. C2×#10587542 | C2 | semidirect |
| 4. C2×C4×#3624 | C2 | semidirect |
| 10. C2×#63243 | C4 | direct (N × H) |
| 18. #10587542 | C22 | semidirect |
| 19. C4×#3624 | C22 | semidirect |
| 34. C2×#3624 | C2×C4 | semidirect |
| 36. #63243 | C2×C4 | direct (N × H) |
| 50. C2×C4×C17 | M16 | semidirect |
| 55. C2×Dic17 | M16 | semidirect |
| 65. #3624 | C22×C4 | semidirect |
| 77. C4×C17 | C2×M16 | semidirect |
| 80. Dic17 | C2×M16 | semidirect |
| 87. C2×C17 | C4×M16 | semidirect |
| 106. C17 | C2×C4×M16 | semidirect |
| 147. C2×C4 | #63243 | direct (N × H) |
| 166. C4 | C2×#63243 | direct (N × H) |
| 169. C2 | C4×#63243 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63243 | 2 |
| C4×#63243 | 2 |
| C2×#10587542 | 2 |
| C2×C4×#3624 | 2 |
| C2×C42×D17 | 2 |
| C2×C4×M16 | 17 |