Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
252 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 72 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 | semidirect |
| 44. Q8×C17 | M16 | semidirect |
| 96. C17 | #1491 | semidirect |
| 121. Q8 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763830 | 2 |
| C4×#63247 | 2 |
| Q8⋊#3624 | 2 |
| C2×Q8×Dic17 | 2 |
| #1491 | 17 |