Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#17984121 | C2 | semidirect |
| 2. C2×#17984096 | C2 | semidirect |
| 4. #22577979 | C2 | semidirect |
| 5. #22577662 | C2 | semidirect |
| 6. #22577650 | C2 | semidirect |
| 7. #22577645 | C2 | semidirect |
| 8. #22577633 | C2 | semidirect |
| 9. #22577397 | C2 | semidirect |
| 10. C2×#17984011 | C2 | semidirect |
| 11. #428×C137 | C2 | semidirect |
| 77. M16×C137 | D4 | semidirect |
| 143. C137 | #3063 | semidirect |
| 153. #428 | D137 | semidirect |
| 210. M16 | D548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984121 | 2 |
| C2×#17984096 | 2 |
| #22577984 | 2 |
| #22577979 | 2 |
| #22577662 | 2 |
| #22577650 | 2 |
| #22577645 | 2 |
| #22577633 | 2 |
| #22577397 | 2 |
| C2×#17984011 | 2 |
| #428×C137 | 2 |
| #3063 | 137 |