Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
320 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. M16×#10587739 | C2 | semidirect |
| 4. #22578339 | C2 | semidirect |
| 5. #22578275 | C2 | semidirect |
| 6. #22578274 | C2 | semidirect |
| 9. Q8×#10587739 | C4 | semidirect |
| 11. D4×#10587739 | C4 | semidirect |
| 17. #17984153 | C4 | semidirect |
| 18. #17984152 | C4 | semidirect |
| 25. #17984016 | C4 | semidirect |
| 26. #17984015 | C4 | semidirect |
| 27. #17984014 | C4 | semidirect |
| 28. #104×C137 | C4 | semidirect |
| 32. #14555520 | C2×C4 | semidirect |
| 43. C4×#10587739 | C2×C4 | semidirect |
| 57. #14555494 | C2×C4 | semidirect |
| 61. C4×Dic137 | C2×C4 | semidirect |
| 63. M16×C137 | C2×C4 | semidirect |
| 64. C42×C137 | C2×C4 | semidirect |
| 126. C137 | #1759 | semidirect |
| 152. #104 | #10587739 | semidirect |
| 175. M16 | C2×#10587739 | semidirect |
| 191. C42 | C2×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#10587739 | 2 |
| D137⋊#104 | 2 |
| M16×#10587739 | 2 |
| #22578339 | 2 |
| #22578275 | 2 |
| #22578274 | 2 |
| #104×D137 | 2 |
| #1759 | 137 |