Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×C22⋊D17 |
| commutator, cosocle | C4×C17 | C25 |
| Frattini | C4 | C24×D17 |
| Fitting | C17×#585 | C2 |
| socle | C2×C17 | C23×D4 |
| hypercenter | #585 | D17 |
| hypocenter | C17 | #3586 |
| LCS | G ▷ C4×C17 ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10587697 | C2 | semidirect |
| 2. #11763624 | C2 | semidirect |
| 3. #11763620 | C2 | semidirect |
| 4. #11763607 | C2 | semidirect |
| 5. C2×#10587637 | C2 | semidirect |
| 6. #11763576 | C2 | semidirect |
| 7. C17×#585 | C2 | semidirect |
| 9. C17×2−1+4 | C22 | semidirect |
| 11. C17×H(5,𝔽2) | C22 | semidirect |
| 16. #10587697 | C22 | semidirect |
| 19. C2×#63252 | C22 | semidirect |
| 20. C22×Dic34 | C22 | semidirect |
| 21. #10587637 | C22 | semidirect |
| 22. #10587637 | C22 | semidirect |
| 23. #10587636 | C22 | semidirect |
| 24. #10587635 | C22 | semidirect |
| 25. #10587634 | C22 | semidirect |
| 26. C2×#63231 | C22 | semidirect |
| 27. #10587628 | C22 | semidirect |
| 28. C2×#63229 | C22 | semidirect |
| 29. #10587618 | C22 | semidirect |
| 30. C2×#63223 | C22 | semidirect |
| 108. #585 | D17 | semidirect |
| 123. 2−1+4 | C2×D17 | semidirect |
| 125. H(5,𝔽2) | C2×D17 | semidirect |
| 143. C17 | #3586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587697 | 2 |
| #11763624 | 2 |
| #11763620 | 2 |
| #11763607 | 2 |
| C2×#10587637 | 2 |
| #11763576 | 2 |
| C17×#585 | 2 |
| #3586 | 17 |