Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
248 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22576207 | C2 | semidirect |
| 2. #22576191 | C2 | semidirect |
| 3. #22576190 | C2 | semidirect |
| 4. #22576180 | C2 | semidirect |
| 5. C2×#16864644 | C2 | semidirect |
| 6. #22576167 | C2 | semidirect |
| 7. 2−1+4×C271 | C2 | semidirect |
| 52. C271 | #578 | semidirect |
| 55. 2−1+4 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22576207 | 2 |
| #22576191 | 2 |
| #22576190 | 2 |
| #22576180 | 2 |
| C2×#16864644 | 2 |
| #22576167 | 2 |
| 2−1+4×C271 | 2 |
| #578 | 271 |