Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 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×#125 | C2 |
| prime radical | C2×D68 | C22 |
| hypercenter | #125 | D17 |
| hypocenter | C17 | #554 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×#125 | C2 | semidirect |
| 2. #10587583 | C2 | semidirect |
| 3. #10587582 | C2 | semidirect |
| 4. #10587582 | C2 | semidirect |
| 7. C4⋊C4×D17 | C2 | semidirect |
| 8. #10587576 | C2 | semidirect |
| 9. #10587574 | C2 | semidirect |
| 11. C4×Dic34 | C2 | semidirect |
| 46. D68 | Q8 | semidirect |
| 73. #125 | D17 | semidirect |
| 82. C17 | #554 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#125 | 2 |
| #10587583 | 2 |
| #10587582 | 2 |
| #10587579 | 2 |
| C4⋊C4×D17 | 2 |
| #10587576 | 2 |
| #10587574 | 2 |
| C4×D68 | 2 |
| C4×Dic34 | 2 |
| #554 | 17 |