Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
442 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 76 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. C22×C4×#10587739 | C2 | semidirect |
| 2. C2×#17984153 | C2 | semidirect |
| 3. #22578374 | C2 | semidirect |
| 4. #22578273 | C2 | semidirect |
| 17. #17984064 | C4 | semidirect |
| 18. #17984063 | C4 | semidirect |
| 19. #17984062 | C4 | semidirect |
| 24. C22⋊Q8×C137 | C4 | semidirect |
| 34. C4×#10587739 | D4 | semidirect |
| 40. C2×D548 | C2×C4 | semidirect |
| 50. C4⋊Dic137 | C2×C4 | semidirect |
| 57. C2×Q8×C137 | C2×C4 | semidirect |
| 60. C4⋊C4×C137 | C2×C4 | semidirect |
| 99. C22×C137 | #104 | semidirect |
| 110. C2×D137 | #104 | semidirect |
| 129. C137 | #1896 | semidirect |
| 142. C22⋊Q8 | #10587739 | semidirect |
| 158. C2×Q8 | C2×#10587739 | semidirect |
| 182. C4⋊C4 | C2×#10587739 | semidirect |
| 241. C22 | #17984153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#10587739 | 2 |
| C2×#17984153 | 2 |
| #22578374 | 2 |
| #22578273 | 2 |
| #22577916 | 2 |
| #1896 | 137 |