Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
316 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
|---|---|---|
| 13. #10587544 | C4 | direct (N × H) |
| 28. C4×Dic17 | C8 | semidirect |
| 29. C4×Dic17 | C8 | semidirect |
| 67. C4×C17 | C4⋊C8 | semidirect |
| 69. Dic17 | C4×C8 | semidirect |
| 70. Dic17 | C4⋊C8 | semidirect |
| 94. C17 | C4×C4⋊C8 | semidirect |
| 151. C4 | #10587544 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587544 | 2 |
| C2×C4×#3624 | 2 |
| #11763675 | 2 |
| C42×Dic17 | 2 |
| C4×C4⋊C8 | 17 |