Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
238 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 95 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 | C23×D17 |
| commutator, socle, cosocle | C22×C17 | C24 |
| Fitting | C17×#126 | C2 |
| hypercenter | #126 | D17 |
| hypocenter | C17 | #553 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×#126 | C2 | semidirect |
| 2. #10587584 | C2 | semidirect |
| 3. #10587581 | C2 | semidirect |
| 4. #10587580 | C2 | semidirect |
| 5. #10587579 | C2 | semidirect |
| 6. C4⋊C4×D17 | C2 | semidirect |
| 7. #10587575 | C2 | semidirect |
| 8. #10587572 | C2 | semidirect |
| 9. #10587570 | C2 | semidirect |
| 10. #10587570 | C2 | semidirect |
| 11. #10587570 | C2 | semidirect |
| 12. #10587567 | C2 | semidirect |
| 13. #10587567 | C2 | semidirect |
| 14. C4×D68 | C2 | semidirect |
| 15. #10587558 | C2 | semidirect |
| 111. #126 | D17 | semidirect |
| 125. C17 | #553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#126 | 2 |
| #10587584 | 2 |
| #10587581 | 2 |
| #10587580 | 2 |
| #10587579 | 2 |
| C4⋊C4×D17 | 2 |
| #10587575 | 2 |
| #10587572 | 2 |
| #10587570 | 2 |
| #10587567 | 2 |
| C4×D68 | 2 |
| #10587558 | 2 |
| #553 | 17 |