Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22577871 | C2 | semidirect |
| 3. #22577419 | C2 | semidirect |
| 4. C2×#17984014 | C2 | semidirect |
| 5. #22577376 | C2 | semidirect |
| 6. #22577164 | C2 | semidirect |
| 7. #344×C137 | C2 | semidirect |
| 11. #17984121 | C4 | semidirect |
| 13. #17984116 | C4 | semidirect |
| 37. C2×Dic274 | C2×C4 | semidirect |
| 39. C2×D548 | C2×C4 | semidirect |
| 64. M16×C137 | C2×C4 | semidirect |
| 129. C137 | #1906 | semidirect |
| 136. #344 | D137 | semidirect |
| 185. M16 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578203 | 2 |
| #22577871 | 2 |
| #22577419 | 2 |
| C2×#17984014 | 2 |
| #22577376 | 2 |
| #22577164 | 2 |
| #344×C137 | 2 |
| #1906 | 137 |