Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. C2×#17984547 | C2 | semidirect |
| 3. #22579808 | C2 | direct (N × H) |
| 4. C2×C42×C277 | C2 | semidirect |
| 7. #17984563 | C4 | semidirect |
| 9. C2×Dic554 | C4 | semidirect |
| 10. C2×D1108 | C4 | semidirect |
| 14. #17984547 | C22 | semidirect |
| 19. C42×C277 | C22 | semidirect |
| 22. Dic554 | C2×C4 | semidirect |
| 24. D1108 | C2×C4 | semidirect |
| 54. C2×C277 | #104 | semidirect |
| 57. C277 | C2×#104 | semidirect |
| 61. C2×C42 | D277 | semidirect |
| 77. C42 | C2×D277 | semidirect |
| 113. C2 | #22579808 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984563 | 2 |
| C2×#17984547 | 2 |
| #22579808 | 2 |
| C2×C42×C277 | 2 |
| C2×#104 | 277 |