Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22576158 | C2 | semidirect |
| 2. #22576150 | C2 | semidirect |
| 3. #22576150 | C2 | semidirect |
| 4. #22576138 | C2 | semidirect |
| 5. #22576138 | C2 | semidirect |
| 6. #22576137 | C2 | semidirect |
| 7. #22576137 | C2 | semidirect |
| 8. #22576136 | C2 | semidirect |
| 9. #22576125 | C2 | semidirect |
| 13. C2×Dic271⋊C4 | C2 | semidirect |
| 14. C4⋊C4×D271 | C2 | semidirect |
| 15. C22⋊Q8×C271 | C2 | semidirect |
| 54. C22⋊D271 | Q8 | semidirect |
| 101. C271 | #554 | semidirect |
| 111. C22⋊Q8 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22576158 | 2 |
| #22576150 | 2 |
| #22576138 | 2 |
| #22576137 | 2 |
| #22576136 | 2 |
| #22576125 | 2 |
| C4×C22⋊D271 | 2 |
| (C22⋊D271)⋊C4 | 2 |
| C2×Dic271⋊C4 | 2 |
| C4⋊C4×D271 | 2 |
| C22⋊Q8×C271 | 2 |
| #554 | 271 |