Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator | C22×C17 | C23×C4 |
| Fitting | C17×#383 | C2 |
| socle, cosocle | C23×C17 | C24 |
| prime radical | C22×D68 | C22 |
| hypercenter | #383 | D17 |
| hypocenter | C17 | #2337 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11762713 | C2 | semidirect |
| 3. #11762701 | C2 | semidirect |
| 4. #11762698 | C2 | semidirect |
| 6. #11762683 | C2 | semidirect |
| 7. C4×C4⋊Dic17 | C2 | semidirect |
| 8. #11762656 | C2 | semidirect |
| 9. C17×#383 | C2 | semidirect |
| 24. #10587561 | C4 | semidirect |
| 47. C2×Dic34 | C2×C4 | semidirect |
| 48. C42×C17 | C2×C4 | semidirect |
| 52. #63227 | C2×C4 | semidirect |
| 53. #63227 | C2×C4 | semidirect |
| 119. #383 | D17 | semidirect |
| 150. C17 | #2337 | semidirect |
| 177. C42 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587561 | 2 |
| #11762713 | 2 |
| #11762701 | 2 |
| #11762698 | 2 |
| #11762687 | 2 |
| #11762683 | 2 |
| C4×C4⋊Dic17 | 2 |
| #11762656 | 2 |
| C17×#383 | 2 |
| #2337 | 17 |