Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
402 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 80 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×#17984151 | C2 | semidirect |
| 4. (C2×#10587739)⋊Q8 | C2 | semidirect |
| 5. #22578277 | C2 | semidirect |
| 6. #22578268 | C2 | semidirect |
| 22. C2×#14555499 | C4 | semidirect |
| 23. C2×#14555498 | C4 | semidirect |
| 24. C2×#14555497 | C4 | semidirect |
| 28. C2×SD16×C137 | C4 | semidirect |
| 48. C2×Dic274 | C2×C4 | semidirect |
| 64. C2×#11764040 | C2×C4 | semidirect |
| 67. C2×Q8×C137 | C2×C4 | semidirect |
| 70. C2×C8×C137 | C2×C4 | semidirect |
| 83. C2×#10587739 | SD16 | semidirect |
| 154. C137 | #1877 | semidirect |
| 171. C2×SD16 | #10587739 | semidirect |
| 191. C2×Q8 | C2×#10587739 | semidirect |
| 218. C2×C8 | C2×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#10587739 | 2 |
| C2×#17984151 | 2 |
| C2×#17984150 | 2 |
| (C2×#10587739)⋊Q8 | 2 |
| #22578277 | 2 |
| #22578268 | 2 |
| C2×SD16×D137 | 2 |
| #1877 | 137 |