Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
440 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 215 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 | direct (N × H) |
| 15. C2×#11764049 | Q8 | direct (N × H) |
| 23. C2×Dic274 | C8 | semidirect |
| 24. Q8×D137 | C8 | semidirect |
| 27. C2×Q8×C137 | C8 | semidirect |
| 29. #11764049 | C2×Q8 | direct (N × H) |
| 37. Dic274 | C2×C8 | semidirect |
| 41. Q8×C137 | C2×C8 | semidirect |
| 54. C2×C137 | C8×Q8 | semidirect |
| 56. D137 | C8×Q8 | semidirect |
| 59. C137 | C2×C8×Q8 | semidirect |
| 77. C2×Q8 | #11764049 | direct (N × H) |
| 90. Q8 | C2×#11764049 | direct (N × H) |
| 117. C2 | Q8×#11764049 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11764049 | 2 |
| C2×C4⋊#11764049 | 2 |
| C2×C4×#11764049 | 2 |
| C2×Q8×#10587739 | 2 |
| C2×C8×Q8 | 137 |