Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 91 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×#123 | C2 |
| hypercenter | #123 | D17 |
| hypocenter | C17 | #562 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×#123 | C2 | semidirect |
| 2. #10587625 | C2 | semidirect |
| 3. #10587624 | C2 | semidirect |
| 4. #10587616 | C2 | semidirect |
| 5. #10587610 | C2 | semidirect |
| 6. #10587583 | C2 | semidirect |
| 7. #10587582 | C2 | semidirect |
| 8. #10587580 | C2 | semidirect |
| 9. #10587576 | C2 | semidirect |
| 10. #10587572 | C2 | semidirect |
| 11. #10587571 | C2 | semidirect |
| 12. #10587571 | C2 | semidirect |
| 13. #10587570 | C2 | semidirect |
| 14. #10587569 | C2 | semidirect |
| 15. #10587564 | C2 | semidirect |
| 116. #123 | D17 | semidirect |
| 125. C17 | #562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#123 | 2 |
| #10587625 | 2 |
| #10587624 | 2 |
| #10587616 | 2 |
| #10587610 | 2 |
| #10587583 | 2 |
| #10587582 | 2 |
| #10587580 | 2 |
| #10587576 | 2 |
| #10587572 | 2 |
| #10587571 | 2 |
| #10587570 | 2 |
| #10587569 | 2 |
| #10587564 | 2 |
| #562 | 17 |