Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 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×#16864638 | C2 | semidirect |
| 2. C2×#16864637 | C2 | semidirect |
| 4. Dic271⋊C8 | C2 | semidirect |
| 5. (C2×D271)⋊C8 | C2 | semidirect |
| 6. C8×Dic271 | C2 | semidirect |
| 7. C22⋊C8×C271 | C2 | semidirect |
| 29. C271⋊C8 | D4 | semidirect |
| 49. Dic271 | M16 | semidirect |
| 55. C271 | #436 | semidirect |
| 62. C22⋊C8 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864638 | 2 |
| C2×#16864637 | 2 |
| C4×C22⋊D271 | 2 |
| Dic271⋊C8 | 2 |
| (C2×D271)⋊C8 | 2 |
| C8×Dic271 | 2 |
| C22⋊C8×C271 | 2 |
| #436 | 271 |