Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
112 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 43 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×#16864644 | C2 | semidirect |
| 4. C4⋊(C271⋊C8) | C2 | semidirect |
| 5. #22576083 | C2 | semidirect |
| 7. C4×Q8×C271 | C2 | semidirect |
| 51. C271 | #464 | semidirect |
| 56. C4×Q8 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864644 | 2 |
| C2×#16864641 | 2 |
| #22576148 | 2 |
| C4⋊(C271⋊C8) | 2 |
| #22576083 | 2 |
| #22576080 | 2 |
| C4×Q8×C271 | 2 |
| #464 | 271 |