Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 165 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. #22577810 | C2 | direct (N × H) |
| 35. C2×#11764040 | Q8 | semidirect |
| 49. C2×C8×C137 | Q8 | semidirect |
| 64. #11764040 | C2×Q8 | semidirect |
| 74. C8×C137 | C2×Q8 | semidirect |
| 88. C2×C137 | #501 | semidirect |
| 92. C137 | C2×#501 | semidirect |
| 133. C2×C8 | Dic274 | semidirect |
| 167. C8 | C2×Dic274 | semidirect |
| 181. C2 | #22577810 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984087 | 2 |
| C2×#17984079 | 2 |
| #22577810 | 2 |
| C2×#17984022 | 2 |
| C2×#17984021 | 2 |
| C2×#17984019 | 2 |
| C2×#17983998 | 2 |
| C2×#106×C137 | 2 |
| C2×#501 | 137 |