Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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. #22577811 | C2 | semidirect |
| 3. #22577809 | C2 | semidirect |
| 4. #22577807 | C2 | semidirect |
| 5. #22577805 | C2 | semidirect |
| 6. #22577804 | C2 | semidirect |
| 11. #500×C137 | C2 | semidirect |
| 42. #14555493 | Q8 | semidirect |
| 45. C8×D137 | Q8 | semidirect |
| 107. C137 | #3164 | semidirect |
| 113. #500 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578030 | 2 |
| #22577811 | 2 |
| #22577809 | 2 |
| #22577807 | 2 |
| #22577805 | 2 |
| #22577804 | 2 |
| #22577444 | 2 |
| #22577440 | 2 |
| #107×D137 | 2 |
| #22577357 | 2 |
| #500×C137 | 2 |
| #3164 | 137 |