Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 3. #22577153 | C2 | semidirect |
| 4. Q8⋊#11764040 | C2 | semidirect |
| 6. C8×#11764040 | C2 | semidirect |
| 7. C8×Q8×C137 | C2 | semidirect |
| 25. #14555497 | C8 | direct (N × H) |
| 50. #11764040 | C2×C8 | semidirect |
| 52. Q8×C137 | C2×C8 | semidirect |
| 60. C8×C137 | SD16 | semidirect |
| 77. C137 | C8×SD16 | semidirect |
| 79. C8×Q8 | D137 | semidirect |
| 121. Q8 | C8×D137 | semidirect |
| 138. C8 | #14555497 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14555497 | 2 |
| C8×D548 | 2 |
| #22577153 | 2 |
| Q8⋊#11764040 | 2 |
| #22577130 | 2 |
| C8×#11764040 | 2 |
| C8×Q8×C137 | 2 |
| C8×SD16 | 137 |