Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
702 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 149 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 | C17×#379 | C2 |
| prime radical | C2×#10587639 | C2 |
| hypercenter | #379 | D17 |
| hypocenter | C17 | #2622 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C22⋊Dic17 | C2 | semidirect |
| 3. #11762734 | C2 | semidirect |
| 4. #11762725 | C2 | semidirect |
| 5. #11762686 | C2 | semidirect |
| 6. #11762684 | C2 | semidirect |
| 7. C17×#379 | C2 | semidirect |
| 19. C2×#63227 | C22 | semidirect |
| 20. C2×C4⋊Dic17 | C22 | semidirect |
| 21. #10587502 | C22 | semidirect |
| 22. #10587502 | C22 | semidirect |
| 98. #379 | D17 | semidirect |
| 120. C17 | #2622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587639 | 2 |
| C22×C22⋊Dic17 | 2 |
| #11762734 | 2 |
| #11762725 | 2 |
| #11762686 | 2 |
| #11762684 | 2 |
| C17×#379 | 2 |
| #2622 | 17 |