Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
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×Dic554 | C2 | semidirect |
| 2. #22579880 | C2 | semidirect |
| 3. #22579879 | C2 | semidirect |
| 4. #22579859 | C2 | semidirect |
| 5. #22579857 | C2 | semidirect |
| 6. C4×Dic554 | C2 | semidirect |
| 28. Dic554 | D4 | direct (N × H) |
| 34. D4×C277 | Q8 | semidirect |
| 42. C22×C277 | C2×Q8 | semidirect |
| 47. C4×C277 | C2×Q8 | semidirect |
| 55. C277 | D4×Q8 | semidirect |
| 86. D4 | Dic554 | direct (N × H) |
| 98. C22 | C2×Dic554 | semidirect |
| 106. C4 | C2×Dic554 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic554 | 2 |
| #22579880 | 2 |
| #22579879 | 2 |
| #22579859 | 2 |
| #22579857 | 2 |
| C4×Dic554 | 2 |
| D4×Dic277 | 2 |
| C4×D4×C277 | 2 |
| D4×Q8 | 277 |