Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
652 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 182 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. C2×Q8×#10587739 | C2 | semidirect |
| 3. (C2×#10587739)⋊Q8 | C2 | semidirect |
| 5. #22578353 | C2 | semidirect |
| 6. #22578347 | C2 | semidirect |
| 7. C22⋊C4×#10587739 | C2 | semidirect |
| 8. C42×#10587739 | C2 | semidirect |
| 27. #17984077 | C4 | semidirect |
| 28. #17984076 | C4 | semidirect |
| 29. #17984075 | C4 | semidirect |
| 30. #17984074 | C4 | semidirect |
| 33. #124×C137 | C4 | semidirect |
| 52. C2×Dic274 | C2×C4 | semidirect |
| 53. C2×Dic274 | C2×C4 | semidirect |
| 63. C22⋊Dic137 | C2×C4 | semidirect |
| 64. #14555487 | C2×C4 | semidirect |
| 65. #14555487 | C2×C4 | semidirect |
| 66. C4×Dic137 | C2×C4 | semidirect |
| 67. C4×Dic137 | C2×C4 | semidirect |
| 68. C2×Q8×C137 | C2×C4 | semidirect |
| 70. C22⋊C4×C137 | C2×C4 | semidirect |
| 71. C42×C137 | C2×C4 | semidirect |
| 125. #10587739 | #124 | direct (N × H) |
| 139. C137 | C4×#124 | semidirect |
| 157. #124 | #10587739 | direct (N × H) |
| 179. C2×Q8 | C2×#10587739 | semidirect |
| 203. C22⋊C4 | C2×#10587739 | semidirect |
| 211. C42 | C2×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10587739 | 2 |
| C2×D4×#10587739 | 2 |
| (C2×#10587739)⋊Q8 | 2 |
| #22578355 | 2 |
| #22578353 | 2 |
| #22578347 | 2 |
| C22⋊C4×#10587739 | 2 |
| C42×#10587739 | 2 |
| #124×D137 | 2 |
| C4×#124 | 137 |