Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
232 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 74 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. #22578316 | C2 | direct (N × H) |
| 12. C2×Dic548 | C4 | semidirect |
| 16. Q16×D137 | C4 | semidirect |
| 19. C2×Q16×C137 | C4 | semidirect |
| 33. Dic548 | C2×C4 | semidirect |
| 43. Q16×C137 | C2×C4 | semidirect |
| 80. C2×C137 | #358 | semidirect |
| 82. D137 | #358 | semidirect |
| 85. C137 | C2×#358 | semidirect |
| 98. C2×Q16 | #10587739 | semidirect |
| 121. Q16 | C2×#10587739 | semidirect |
| 169. C2 | #22578316 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984161 | 2 |
| C2×#17984157 | 2 |
| #22578316 | 2 |
| C2×Q16×D137 | 2 |
| C2×#358 | 137 |