Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
688 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 688 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 | C22×C17 | C23×C4 |
| Fitting, prime radical | C2×C17×#120 | C2 |
| socle, cosocle | C23×C17 | C24 |
| hypercenter | C2×#120 | D17 |
| hypocenter | C17 | #2375 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11762712 | C2 | semidirect |
| 2. #11762702 | C2 | semidirect |
| 3. #11762689 | C2 | semidirect |
| 4. #11762665 | C2 | semidirect |
| 8. C23×Dic17 | C22 | semidirect |
| 9. C17×#120 | C4 | semidirect |
| 13. C2×C22⋊Dic17 | C22 | semidirect |
| 14. C2×C4⋊Dic17 | C22 | semidirect |
| 15. C2×C4×Dic17 | C22 | semidirect |
| 16. #10587502 | C22 | semidirect |
| 19. C24×C17 | C2×C4 | semidirect |
| 29. C22⋊C4×C17 | C2×C4 | semidirect |
| 85. #120 | Dic17 | semidirect |
| 93. C17 | #2375 | semidirect |
| 96. C24 | C2×Dic17 | semidirect |
| 110. C22⋊C4 | C2×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762712 | 2 |
| #11762702 | 2 |
| #11762689 | 2 |
| #11762665 | 2 |
| C2×C17×#120 | 2 |
| #2375 | 17 |