Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C23×D17 |
| commutator, socle | C2×C17 | C23×C8 |
| Fitting | C17×#504 | C2 |
| prime radical | #41×D17 | C4 |
| cosocle | C8×C17 | C24 |
| hypercenter | #504 | D17 |
| hypocenter | C17 | #3407 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C8 ◁ #504 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11763227 | C2 | semidirect |
| 3. #11763226 | C2 | semidirect |
| 4. #11763225 | C2 | semidirect |
| 5. C2×#10587469 | C2 | semidirect |
| 6. M32×D17 | C2 | semidirect |
| 7. C17×#504 | C2 | semidirect |
| 15. C17×M32 | C22 | semidirect |
| 16. C2×C16×C17 | C22 | semidirect |
| 17. #10587483 | C22 | semidirect |
| 18. C2×#63214 | C22 | semidirect |
| 21. #10587469 | C22 | semidirect |
| 22. #10587469 | C22 | semidirect |
| 23. C16×D17 | C22 | semidirect |
| 73. #504 | D17 | semidirect |
| 92. M32 | C2×D17 | semidirect |
| 95. C2×C16 | C2×D17 | semidirect |
| 96. C17 | #3407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×D17 | 2 |
| #11763227 | 2 |
| #11763226 | 2 |
| #11763225 | 2 |
| C2×#10587469 | 2 |
| M32×D17 | 2 |
| C17×#504 | 2 |
| #3407 | 17 |