Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 2. #22577776 | C2 | semidirect |
| 3. #22577698 | C2 | semidirect |
| 4. #22577694 | C2 | semidirect |
| 5. #22577146 | C2 | semidirect |
| 6. #22577132 | C2 | semidirect |
| 7. Q8⋊C8×C137 | C2 | semidirect |
| 69. Q8×C137 | SD16 | semidirect |
| 98. C137 | #1631 | semidirect |
| 105. Q8⋊C8 | D137 | semidirect |
| 153. Q8 | #14555499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578075 | 2 |
| #22577776 | 2 |
| #22577698 | 2 |
| #22577694 | 2 |
| #22577146 | 2 |
| #22577132 | 2 |
| Q8⋊C8×C137 | 2 |
| #1631 | 137 |