Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
280 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 94 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. #11763659 | C2 | semidirect |
| 4. Q8⋊#3624 | C2 | semidirect |
| 25. Q8×D17 | C8 | semidirect |
| 54. Q8×C17 | C2×C8 | semidirect |
| 74. Dic34 | C2×C8 | semidirect |
| 102. D17 | Q8⋊C8 | semidirect |
| 120. C17 | C2×Q8⋊C8 | semidirect |
| 155. Q8 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763810 | 2 |
| C4×#63242 | 2 |
| #11763659 | 2 |
| Q8⋊#3624 | 2 |
| C4×Q8×D17 | 2 |
| C2×Q8⋊C8 | 17 |