Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. C2×#10587489 | C2 | semidirect |
| 2. C2×#10587503 | C2 | semidirect |
| 3. C2×C8×Dic17 | C2 | semidirect |
| 4. #11762712 | C2 | semidirect |
| 9. C2×D8×C17 | C4 | semidirect |
| 60. C2×Dic17 | D8 | semidirect |
| 61. C8×C17 | C22⋊C4 | semidirect |
| 94. C2×D8 | Dic17 | semidirect |
| 103. C17 | #1970 | semidirect |
| 148. C8 | C22⋊Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587489 | 2 |
| C2×#10587503 | 2 |
| C2×C8×Dic17 | 2 |
| #11762712 | 2 |
| C22×D8×C17 | 2 |
| #1970 | 17 |