Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊C4×C17 | C2 | semidirect |
| 4. #10587610 | C2 | semidirect |
| 5. #10587610 | C2 | semidirect |
| 6. #10587583 | C2 | semidirect |
| 7. #10587582 | C2 | semidirect |
| 8. C4⋊C4×D17 | C2 | semidirect |
| 9. #10587575 | C2 | semidirect |
| 10. #10587574 | C2 | semidirect |
| 11. #10587573 | C2 | semidirect |
| 43. C22⋊D17 | Q8 | semidirect |
| 85. C2×C4⋊C4 | D17 | semidirect |
| 86. C17 | #554 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×C17 | 2 |
| C4×C22⋊D17 | 2 |
| #10587610 | 2 |
| #10587583 | 2 |
| #10587582 | 2 |
| C4⋊C4×D17 | 2 |
| #10587575 | 2 |
| #10587574 | 2 |
| #10587573 | 2 |
| #554 | 17 |