Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
488 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 221 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. C4×#14555500 | C2 | direct (N × H) |
| 10. C2×#14555500 | C4 | direct (N × H) |
| 36. #14555500 | C2×C4 | direct (N × H) |
| 78. C2×C4×C137 | Q16 | semidirect |
| 93. C4×C137 | C2×Q16 | semidirect |
| 98. C2×C137 | C4×Q16 | semidirect |
| 102. C137 | C2×C4×Q16 | semidirect |
| 179. C2×C4 | #14555500 | direct (N × H) |
| 198. C4 | C2×#14555500 | direct (N × H) |
| 201. C2 | C4×#14555500 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555500 | 2 |
| C2×C4×Dic274 | 2 |
| C4×#14555500 | 2 |
| C2×#17984021 | 2 |
| C2×#17984012 | 2 |
| C2×#17984011 | 2 |
| C2×C4×#11764040 | 2 |
| C2×C4×Q8×C137 | 2 |
| C2×C4×Q16 | 137 |