Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
312 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 1. #22578407 | C2 | semidirect |
| 3. C4×C4⋊#10587739 | C2 | semidirect |
| 4. #22578273 | C2 | semidirect |
| 14. Q8×Dic137 | C4 | semidirect |
| 16. C4×D548 | C4 | semidirect |
| 18. #17984050 | C4 | semidirect |
| 23. C4×Q8×C137 | C4 | semidirect |
| 67. D548 | C4⋊C4 | semidirect |
| 83. Q8×C137 | C4⋊C4 | semidirect |
| 101. C4×C137 | #104 | semidirect |
| 115. C137 | #1806 | semidirect |
| 125. C4×Q8 | #10587739 | semidirect |
| 177. Q8 | C4⋊#10587739 | semidirect |
| 222. C4 | #17984153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578407 | 2 |
| C2×#17984153 | 2 |
| C4×C4⋊#10587739 | 2 |
| #22578273 | 2 |
| C4×#14555511 | 2 |
| #1806 | 137 |