Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
280 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×Q8×D277 | C2 | semidirect |
| 3. #22579879 | C2 | semidirect |
| 4. #22579878 | C2 | semidirect |
| 5. #22579860 | C2 | semidirect |
| 6. #22579858 | C2 | semidirect |
| 7. #22579857 | C2 | semidirect |
| 8. #22579845 | C2 | semidirect |
| 11. C22⋊Q8×C277 | C2 | semidirect |
| 41. Dic554 | D4 | semidirect |
| 42. C22⋊D277 | Q8 | semidirect |
| 60. C22×C277 | C2×Q8 | semidirect |
| 64. C2×D277 | C2×Q8 | semidirect |
| 73. Dic277 | C2×Q8 | semidirect |
| 79. C277 | D4×Q8 | semidirect |
| 88. C22⋊Q8 | D277 | semidirect |
| 143. C22 | Q8×D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic554 | 2 |
| C2×Q8×D277 | 2 |
| #22579879 | 2 |
| #22579878 | 2 |
| #22579860 | 2 |
| #22579858 | 2 |
| #22579857 | 2 |
| #22579845 | 2 |
| C4×C22⋊D277 | 2 |
| #22579840 | 2 |
| C22⋊Q8×C277 | 2 |
| D4×Q8 | 277 |