Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
890 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 455 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 | C24×D17 |
| commutator, socle, cosocle | C22×C17 | C25 |
| Fitting | C17×#564 | C2 |
| prime radical | C22×D17 | C24 |
| hypercenter | #564 | D17 |
| hypocenter | C17 | #3556 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ #564 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17⋊#564 | C2 | semidirect |
| 2. #11763536 | C2 | semidirect |
| 5. C17×#564 | C2 | semidirect |
| 55. #564 | D17 | semidirect |
| 78. C17 | #3556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17⋊#564 | 2 |
| #11763536 | 2 |
| #11763418 | 2 |
| #11763365 | 2 |
| C17×#564 | 2 |
| #3556 | 17 |