Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 124 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×#16864637 | C2 | semidirect |
| 2. C2×C8×D271 | C2 | semidirect |
| 4. (C2×D271)⋊C8 | C2 | semidirect |
| 5. (C2×D271)⋊C8 | C2 | semidirect |
| 6. #22576071 | C2 | semidirect |
| 7. C4⋊C8×C271 | C2 | semidirect |
| 31. C271⋊C8 | D4 | semidirect |
| 43. C2×D271 | M16 | semidirect |
| 55. C271 | #435 | semidirect |
| 60. C4⋊C8 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864637 | 2 |
| C2×C8×D271 | 2 |
| C4×D1084 | 2 |
| (C2×D271)⋊C8 | 2 |
| #22576071 | 2 |
| C4⋊C8×C271 | 2 |
| #435 | 271 |