Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 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. #22576158 | C2 | semidirect |
| 6. #22576070 | C2 | semidirect |
| 7. C2×Q16×C271 | C2 | semidirect |
| 49. C271 | #497 | semidirect |
| 52. C2×Q16 | 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×#16864643 | 2 |
| C2×#16864641 | 2 |
| #22576158 | 2 |
| #22576149 | 2 |
| #22576070 | 2 |
| C2×Q16×C271 | 2 |
| #497 | 271 |