Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22576155 | C2 | semidirect |
| 2. #22576151 | C2 | semidirect |
| 3. #22576150 | C2 | semidirect |
| 5. #22576140 | C2 | semidirect |
| 6. #22576139 | C2 | semidirect |
| 7. #22576125 | C2 | semidirect |
| 9. #22576119 | C2 | semidirect |
| 10. #22576118 | C2 | semidirect |
| 11. C2×C4⋊C4×C271 | C2 | semidirect |
| 72. C271 | #552 | semidirect |
| 84. C2×C4⋊C4 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22576155 | 2 |
| #22576151 | 2 |
| #22576150 | 2 |
| #22576143 | 2 |
| #22576140 | 2 |
| #22576139 | 2 |
| #22576125 | 2 |
| C4×C22⋊D271 | 2 |
| #22576119 | 2 |
| #22576118 | 2 |
| C2×C4⋊C4×C271 | 2 |
| #552 | 271 |