Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
236 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 97 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×#124 | C2 |
| prime radical | #10587626 | C2 |
| hypercenter | #124 | D17 |
| hypocenter | C17 | #559 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×#124 | C2 | semidirect |
| 2. #10587633 | C2 | semidirect |
| 3. Q8×Dic17 | C2 | semidirect |
| 5. D4×Dic17 | C2 | semidirect |
| 6. #10587572 | C2 | semidirect |
| 7. #10587571 | C2 | semidirect |
| 8. #10587569 | C2 | semidirect |
| 9. #10587567 | C2 | semidirect |
| 10. C4×D68 | C2 | semidirect |
| 11. C4×Dic34 | C2 | semidirect |
| 79. #124 | D17 | semidirect |
| 87. C17 | #559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#124 | 2 |
| #10587633 | 2 |
| Q8×Dic17 | 2 |
| #10587626 | 2 |
| D4×Dic17 | 2 |
| #10587572 | 2 |
| #10587571 | 2 |
| #10587569 | 2 |
| #10587567 | 2 |
| C4×D68 | 2 |
| C4×Dic34 | 2 |
| #559 | 17 |