Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
356 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 153 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. #22577807 | C2 | semidirect |
| 3. #22577804 | C2 | semidirect |
| 4. #22577803 | C2 | semidirect |
| 5. #22577800 | C2 | semidirect |
| 31. C2×#11764040 | Q8 | semidirect |
| 44. C2×C8×C137 | Q8 | semidirect |
| 78. C137 | #3160 | semidirect |
| 114. C2×C8 | Dic274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577956 | 2 |
| #22577807 | 2 |
| #22577804 | 2 |
| #22577803 | 2 |
| #22577800 | 2 |
| #22577441 | 2 |
| #22577439 | 2 |
| C2×C8×Dic137 | 2 |
| #427×C137 | 2 |
| #3160 | 137 |