Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
552 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 245 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×Q8×Dic137 | C2 | semidirect |
| 3. SD16×Dic137 | C2 | direct (N × H) |
| 4. C2×#17984020 | C2 | semidirect |
| 5. C2×#17984012 | C2 | semidirect |
| 7. C2×C8×Dic137 | C2 | semidirect |
| 12. Q8×Dic137 | C22 | semidirect |
| 21. #17984020 | C22 | semidirect |
| 22. #17984012 | C22 | semidirect |
| 24. C8×Dic137 | C22 | semidirect |
| 27. C2×SD16×C137 | C4 | semidirect |
| 50. C2×Q8×C137 | C2×C4 | semidirect |
| 58. SD16×C137 | C2×C4 | semidirect |
| 59. C2×C8×C137 | C2×C4 | semidirect |
| 67. C2×Dic137 | SD16 | direct (N × H) |
| 78. Q8×C137 | C22×C4 | semidirect |
| 88. C8×C137 | C22×C4 | semidirect |
| 104. Dic137 | C2×SD16 | direct (N × H) |
| 106. C2×C137 | C4×SD16 | semidirect |
| 110. C137 | C2×C4×SD16 | semidirect |
| 123. C2×SD16 | Dic137 | direct (N × H) |
| 144. C2×Q8 | C2×Dic137 | semidirect |
| 158. SD16 | C2×Dic137 | direct (N × H) |
| 161. C2×C8 | C2×Dic137 | semidirect |
| 179. Q8 | C22×Dic137 | semidirect |
| 199. C8 | C22×Dic137 | semidirect |
| 217. C2 | SD16×Dic137 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic137 | 2 |
| C2×D4×Dic137 | 2 |
| SD16×Dic137 | 2 |
| C2×#17984020 | 2 |
| C2×#17984012 | 2 |
| C2×#17984009 | 2 |
| C2×C8×Dic137 | 2 |
| C22×SD16×C137 | 2 |
| C2×C4×SD16 | 137 |