Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 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. Q8×#11764049 | C2 | semidirect |
| 3. #22578493 | C2 | semidirect |
| 4. Q8⋊#11764049 | C2 | semidirect |
| 6. #22578487 | C2 | semidirect |
| 39. #14555499 | C8 | semidirect |
| 40. #14555498 | C8 | semidirect |
| 41. #14555497 | C8 | semidirect |
| 43. SD16×C137 | C8 | semidirect |
| 58. Dic274 | C2×C8 | semidirect |
| 63. #11764040 | C2×C8 | semidirect |
| 64. Q8×C137 | C2×C8 | semidirect |
| 66. C8×C137 | C2×C8 | semidirect |
| 86. C137 | SD16⋊C8 | semidirect |
| 116. SD16 | #11764049 | semidirect |
| 134. Q8 | C2×#11764049 | semidirect |
| 153. C8 | C2×#11764049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11764049 | 2 |
| D4×#11764049 | 2 |
| #22578493 | 2 |
| Q8⋊#11764049 | 2 |
| D4⋊#11764049 | 2 |
| #22578487 | 2 |
| SD16×#10587739 | 2 |
| SD16⋊C8 | 137 |