Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
280 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 123 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. C22×Dic542 | C2 | semidirect |
| 2. #22576160 | C2 | semidirect |
| 3. #22576159 | C2 | semidirect |
| 4. #22576139 | C2 | semidirect |
| 5. #22576137 | C2 | semidirect |
| 6. C4×Dic542 | C2 | semidirect |
| 28. Dic542 | D4 | direct (N × H) |
| 34. D4×C271 | Q8 | semidirect |
| 42. C22×C271 | C2×Q8 | semidirect |
| 47. C4×C271 | C2×Q8 | semidirect |
| 55. C271 | D4×Q8 | semidirect |
| 86. D4 | Dic542 | direct (N × H) |
| 98. C22 | C2×Dic542 | semidirect |
| 106. C4 | C2×Dic542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic542 | 2 |
| #22576160 | 2 |
| #22576159 | 2 |
| #22576139 | 2 |
| #22576137 | 2 |
| C4×Dic542 | 2 |
| D4×Dic271 | 2 |
| C4×D4×C271 | 2 |
| D4×Q8 | 271 |