Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
726 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 200 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. D137⋊#131 | C2 | semidirect |
| 2. #22578472 | C2 | semidirect |
| 3. #22578396 | C2 | semidirect |
| 4. #22578394 | C2 | semidirect |
| 5. #22578393 | C2 | semidirect |
| 6. C2×#17984151 | C2 | semidirect |
| 22. #17984136 | C4 | semidirect |
| 24. #17984135 | C4 | semidirect |
| 25. #17984135 | C4 | semidirect |
| 31. 2−1+4×C137 | C4 | semidirect |
| 45. #14555511 | C2×C4 | semidirect |
| 51. #14555510 | C2×C4 | semidirect |
| 55. #14555509 | C2×C4 | semidirect |
| 59. C2×Dic274 | C2×C4 | semidirect |
| 64. Q8×D137 | C2×C4 | semidirect |
| 75. #41×C137 | C2×C4 | semidirect |
| 77. C2×Q8×C137 | C2×C4 | semidirect |
| 141. C137 | #2898 | semidirect |
| 155. 2−1+4 | #10587739 | semidirect |
| 189. #41 | C2×#10587739 | semidirect |
| 201. C2×Q8 | C2×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D137⋊#131 | 2 |
| #22578472 | 2 |
| #22578396 | 2 |
| #22578394 | 2 |
| #22578393 | 2 |
| C2×#17984151 | 2 |
| 2−1+4×D137 | 2 |
| #2898 | 137 |