Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #22577675 | C2 | direct (N × H) |
| 4. C2×#17984024 | C2 | semidirect |
| 5. C2×#17984007 | C2 | semidirect |
| 6. C22×Q16×C137 | C2 | semidirect |
| 18. #17984024 | C22 | semidirect |
| 19. #17984007 | C22 | semidirect |
| 24. C2×Q16×C137 | C22 | semidirect |
| 100. C2×C137 | #473 | semidirect |
| 103. C137 | C2×#473 | semidirect |
| 106. C22×Q16 | D137 | semidirect |
| 119. C2×Q16 | C2×D137 | semidirect |
| 205. C2 | #22577675 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984119 | 2 |
| C2×#17984094 | 2 |
| #22577675 | 2 |
| C2×#17984024 | 2 |
| C2×#17984007 | 2 |
| C22×Q16×C137 | 2 |
| C2×#473 | 137 |