Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
852 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Fitting | C23×Q8×C17 | C2 |
| prime radical | C2×#10587616 | C2 |
| hypercenter | C23×Q8 | D17 |
| hypocenter | C17 | #2436 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10587633 | C2 | semidirect |
| 3. #11762720 | C2 | semidirect |
| 4. #11762716 | C2 | semidirect |
| 5. #11762688 | C2 | semidirect |
| 6. C4×C22⋊Dic17 | C2 | semidirect |
| 7. C23×Q8×C17 | C2 | semidirect |
| 32. C2×Q8×C17 | D4 | semidirect |
| 82. C22×C17 | #124 | semidirect |
| 96. C23×Q8 | D17 | semidirect |
| 126. C17 | #2436 | semidirect |
| 134. C2×Q8 | C22⋊D17 | semidirect |
| 187. C22 | #10587633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587633 | 2 |
| C2×#10587616 | 2 |
| #11762720 | 2 |
| #11762716 | 2 |
| #11762688 | 2 |
| C4×C22⋊Dic17 | 2 |
| C23×Q8×C17 | 2 |
| #2436 | 17 |