Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
264 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22578516 | C2 | semidirect |
| 2. C2×C4⋊#11764049 | C2 | semidirect |
| 3. Q8⋊#11764049 | C2 | semidirect |
| 4. D4⋊#11764049 | C2 | semidirect |
| 44. #14555511 | C8 | semidirect |
| 46. #14555510 | C8 | semidirect |
| 48. #14555509 | C8 | semidirect |
| 54. #41×C137 | C8 | semidirect |
| 72. Dic274 | C2×C8 | semidirect |
| 74. D548 | C2×C8 | semidirect |
| 87. Q8×C137 | C2×C8 | semidirect |
| 89. D4×C137 | C2×C8 | semidirect |
| 121. C137 | #1477 | semidirect |
| 150. #41 | #11764049 | semidirect |
| 181. Q8 | C2×#11764049 | semidirect |
| 188. D4 | C2×#11764049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578516 | 2 |
| C2×C4⋊#11764049 | 2 |
| Q8⋊#11764049 | 2 |
| D4⋊#11764049 | 2 |
| #41×#10587739 | 2 |
| #1477 | 137 |