Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
188 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 51 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×#16864642 | C2 | semidirect |
| 2. #22576139 | C2 | semidirect |
| 3. #22576081 | C2 | semidirect |
| 4. C22⋊(C271⋊C8) | C2 | semidirect |
| 6. C2×Dic542 | C22 | semidirect |
| 8. C2×C271⋊C8 | C22 | semidirect |
| 9. C4⋊Dic271 | C22 | semidirect |
| 38. C22×C271 | SD16 | semidirect |
| 49. C271 | #450 | semidirect |
| 88. C22 | #16864642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864642 | 2 |
| #22576139 | 2 |
| #22576081 | 2 |
| C22⋊(C271⋊C8) | 2 |
| C22×D4×C271 | 2 |
| #450 | 271 |