Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
448 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#17984079 | C2 | semidirect |
| 3. #22577706 | C2 | direct (N × H) |
| 4. C2×#17984019 | C2 | semidirect |
| 5. C2×#17984017 | C2 | semidirect |
| 8. C2×#107×C137 | C2 | semidirect |
| 13. #17984079 | C22 | semidirect |
| 21. #17984019 | C22 | semidirect |
| 22. #17984017 | C22 | semidirect |
| 28. #107×C137 | C22 | semidirect |
| 98. C2×C137 | #478 | semidirect |
| 103. C137 | C2×#478 | semidirect |
| 108. C2×#107 | D137 | semidirect |
| 128. #107 | C2×D137 | semidirect |
| 203. C2 | #22577706 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984079 | 2 |
| C2×#17984050 | 2 |
| #22577706 | 2 |
| C2×#17984019 | 2 |
| C2×#17984017 | 2 |
| C2×#17984010 | 2 |
| C2×#17984008 | 2 |
| C2×#107×C137 | 2 |
| C2×#478 | 137 |