Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
280 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 87 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⋊#3633 | C2 | direct (N × H) |
| 27. C2×Q8×C17 | C8 | semidirect |
| 30. Q8×D17 | C8 | semidirect |
| 35. C2×Dic34 | C8 | semidirect |
| 59. Q8×C17 | C2×C8 | semidirect |
| 73. Dic34 | C2×C8 | semidirect |
| 96. C2×C17 | Q8⋊C8 | semidirect |
| 98. D17 | Q8⋊C8 | semidirect |
| 116. C17 | C2×Q8⋊C8 | semidirect |
| 123. C2×Q8 | #3633 | semidirect |
| 149. Q8 | C2×#3633 | semidirect |
| 191. C2 | Q8⋊#3633 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#3633 | 2 |
| C2×C4×#3633 | 2 |
| Q8⋊#3633 | 2 |
| C2×Q8×#595 | 2 |
| C2×Q8⋊C8 | 17 |