Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
280 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 114 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. Q8⋊#3624 | C2 | direct (N × H) |
| 22. C2×Q8×C17 | C8 | semidirect |
| 46. Q8×C17 | C2×C8 | semidirect |
| 83. C2×C17 | Q8⋊C8 | semidirect |
| 102. C17 | C2×Q8⋊C8 | semidirect |
| 105. C2×Q8 | #3624 | semidirect |
| 129. Q8 | C2×#3624 | semidirect |
| 161. C2 | Q8⋊#3624 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#3624 | 2 |
| C2×C4×#3624 | 2 |
| Q8⋊#3624 | 2 |
| C2×Q8×Dic17 | 2 |
| C2×Q8⋊C8 | 17 |