Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C2×#10587476 | C2 | semidirect |
| 3. #11762811 | C2 | semidirect |
| 4. #11762810 | C2 | semidirect |
| 5. C2×#10587494 | C2 | semidirect |
| 6. #11762711 | C2 | semidirect |
| 7. C2×C17×#104 | C2 | semidirect |
| 12. #10587696 | C4 | semidirect |
| 20. C2×M16×C17 | C22 | semidirect |
| 21. C2×C42×C17 | C22 | semidirect |
| 23. C2×C4⋊Dic17 | C22 | semidirect |
| 24. C2×#63223 | C22 | semidirect |
| 95. Q8×C17 | C22⋊C4 | semidirect |
| 99. D4×C17 | C22⋊C4 | semidirect |
| 124. D68 | C22⋊C4 | semidirect |
| 129. Dic34 | C22⋊C4 | semidirect |
| 160. C2×#104 | D17 | semidirect |
| 186. C2×M16 | C2×D17 | semidirect |
| 189. C2×C42 | C2×D17 | semidirect |
| 197. C17 | #1792 | semidirect |
| 263. Q8 | #63227 | semidirect |
| 277. D4 | #63227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587696 | 2 |
| C2×#10587476 | 2 |
| #11762811 | 2 |
| #11762810 | 2 |
| C2×#10587494 | 2 |
| #11762711 | 2 |
| C2×C17×#104 | 2 |
| #1792 | 17 |