Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 53 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. #22578525 | C2 | semidirect |
| 2. #22578524 | C2 | semidirect |
| 3. #22578507 | C2 | semidirect |
| 4. #22578504 | C2 | semidirect |
| 5. #22578503 | C2 | semidirect |
| 6. #10587739⋊C16 | C2 | semidirect |
| 71. C137 | #2170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578525 | 2 |
| #22578524 | 2 |
| #22578507 | 2 |
| #22578504 | 2 |
| #22578503 | 2 |
| #10587739⋊C16 | 2 |
| #22578446 | 2 |
| #2170 | 137 |