Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22579879 | C2 | semidirect |
| 2. #22579878 | C2 | semidirect |
| 3. #22579870 | C2 | semidirect |
| 7. C4×Dic554 | C2 | semidirect |
| 8. C4×Dic554 | C2 | semidirect |
| 11. C4×Q8×C277 | C2 | semidirect |
| 45. C4×D277 | Q8 | semidirect |
| 70. C277 | #533 | semidirect |
| 80. C4×Q8 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22579879 | 2 |
| #22579878 | 2 |
| #22579870 | 2 |
| #22579860 | 2 |
| #22579858 | 2 |
| #22579856 | 2 |
| C4×Dic554 | 2 |
| #22579837 | 2 |
| C42×D277 | 2 |
| C4×Q8×C277 | 2 |
| #533 | 277 |