Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. C2×Q8×Dic137 | C2 | semidirect |
| 4. #22577506 | C2 | direct (N × H) |
| 5. C2×#17984021 | C2 | semidirect |
| 7. C2×#17983998 | C2 | semidirect |
| 8. C2×#103×C137 | C2 | semidirect |
| 11. C2×#14555497 | C4 | semidirect |
| 15. Q8×Dic137 | C22 | semidirect |
| 23. #17984021 | C22 | semidirect |
| 25. #17983998 | C22 | semidirect |
| 29. #103×C137 | C22 | semidirect |
| 40. #14555497 | C2×C4 | semidirect |
| 41. C2×#11764040 | C2×C4 | semidirect |
| 52. C2×Q8×C137 | C2×C4 | semidirect |
| 75. #11764040 | C22×C4 | semidirect |
| 79. Q8×C137 | C22×C4 | semidirect |
| 105. C2×C137 | #440 | semidirect |
| 110. C137 | C2×#440 | semidirect |
| 117. C2×#103 | D137 | semidirect |
| 138. #103 | C2×D137 | semidirect |
| 144. C2×Q8 | C4×D137 | semidirect |
| 179. Q8 | C2×C4×D137 | semidirect |
| 217. C2 | #22577506 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555497 | 2 |
| C2×Q8×Dic137 | 2 |
| C2×#17984050 | 2 |
| #22577506 | 2 |
| C2×#17984021 | 2 |
| C2×#17984010 | 2 |
| C2×#17983998 | 2 |
| C2×#103×C137 | 2 |
| C2×#440 | 137 |