Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
392 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #22577751 | C2 | semidirect |
| 3. #22577690 | C2 | semidirect |
| 4. #22577603 | C2 | semidirect |
| 5. Q8×#11764040 | C2 | semidirect |
| 6. C4×#14555497 | C2 | semidirect |
| 7. Q82×C137 | C2 | semidirect |
| 54. Q8×C137 | SD16 | semidirect |
| 55. Q8×C137 | #41 | semidirect |
| 76. C137 | #3362 | semidirect |
| 78. Q82 | D137 | semidirect |
| 123. Q8 | #14555497 | semidirect |
| 124. Q8 | #14555511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578075 | 2 |
| #22577751 | 2 |
| #22577690 | 2 |
| #22577603 | 2 |
| Q8×#11764040 | 2 |
| C4×#14555497 | 2 |
| Q82×C137 | 2 |
| #3362 | 137 |