Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
988 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 988 conjugacy classes of subgroups — too many to draw. Only its 549 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 | C4×#41×C17 | C2 |
| prime radical | C2×#41×C17 | C22 |
| hypercenter | C4×#41 | D17 |
| hypocenter | C17 | #3504 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11763535 | C2 | semidirect |
| 2. #11763518 | C2 | semidirect |
| 3. #11763437 | C2 | semidirect |
| 4. #11763366 | C2 | semidirect |
| 5. C2×#10587556 | C2 | semidirect |
| 28. #41×C17 | Q8 | semidirect |
| 102. C17 | #3504 | semidirect |
| 103. #41 | Dic34 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763535 | 2 |
| #11763518 | 2 |
| #11763437 | 2 |
| #11763366 | 2 |
| C2×#10587556 | 2 |
| #11763292 | 2 |
| C4×#41×C17 | 2 |
| #3504 | 17 |