Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1102 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 213 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 | C24×C4×C17 | C2 |
| prime radical | C2×#10587639 | C2 |
| hypercenter | C24×C4 | D17 |
| hypocenter | C17 | #2849 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10587615 | C2 | semidirect |
| 3. #11762688 | C2 | semidirect |
| 4. #11762682 | C2 | semidirect |
| 5. #11762672 | C2 | semidirect |
| 6. #11762665 | C2 | semidirect |
| 7. C24×C4×C17 | C2 | semidirect |
| 21. C2×#63227 | C22 | semidirect |
| 22. C2×#63225 | C22 | semidirect |
| 23. #10587502 | C22 | semidirect |
| 35. C22×C4×C17 | D4 | semidirect |
| 85. C22×C17 | #123 | semidirect |
| 96. C24×C4 | D17 | semidirect |
| 125. C17 | #2849 | semidirect |
| 144. C22×C4 | C22⋊D17 | semidirect |
| 188. C22 | #10587615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587615 | 2 |
| C2×#10587639 | 2 |
| #11762688 | 2 |
| #11762682 | 2 |
| #11762672 | 2 |
| #11762665 | 2 |
| C24×C4×C17 | 2 |
| #2849 | 17 |