Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
484 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#595 |
| commutator, socle | C22×C17 | C23×C4 |
| Fitting | C17×#125 | C4 |
| prime radical, cosocle | C22×D17 | C24 |
| hypercenter | #125 | #595 |
| hypocenter | C17 | C4×#125 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. C17×#125 | C4 | semidirect |
| 18. #10587576 | C4 | semidirect |
| 19. #10587575 | C4 | semidirect |
| 21. #10587556 | C4 | semidirect |
| 81. #595 | #125 | direct (N × H) |
| 103. #125 | #595 | direct (N × H) |
| 117. C17 | C4×#125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763760 | 2 |
| #11763758 | 2 |
| #11763753 | 2 |
| C4⋊C4×#595 | 2 |
| C42×#595 | 2 |
| #125×D17 | 2 |
| C4×#125 | 17 |