Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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×#17984050 | C2 | semidirect |
| 3. #22577514 | C2 | direct (N × H) |
| 4. C2×#17984008 | C2 | semidirect |
| 5. C2×#17983998 | C2 | semidirect |
| 6. C2×#106×C137 | C2 | semidirect |
| 9. C2×D1096 | C4 | semidirect |
| 13. #17984050 | C22 | semidirect |
| 16. #17984008 | C22 | semidirect |
| 17. #17983998 | C22 | semidirect |
| 20. #106×C137 | C22 | semidirect |
| 24. C2×D548 | C2×C4 | semidirect |
| 29. D1096 | C2×C4 | semidirect |
| 37. C2×C8×C137 | C2×C4 | semidirect |
| 47. D548 | C22×C4 | semidirect |
| 59. C8×C137 | C22×C4 | semidirect |
| 72. C2×C137 | #442 | semidirect |
| 76. C137 | C2×#442 | semidirect |
| 81. C2×#106 | D137 | semidirect |
| 95. #106 | C2×D137 | semidirect |
| 111. C2×C8 | C4×D137 | semidirect |
| 136. C8 | C2×C4×D137 | semidirect |
| 150. C2 | #22577514 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1096 | 2 |
| C2×#17984050 | 2 |
| #22577514 | 2 |
| C2×#17984008 | 2 |
| C2×#17983998 | 2 |
| C2×#106×C137 | 2 |
| C2×#442 | 137 |