Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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. #22577846 | C2 | semidirect |
| 3. C2×#17984033 | C2 | semidirect |
| 4. #22577678 | C2 | semidirect |
| 5. #22577217 | C2 | semidirect |
| 6. #22577211 | C2 | semidirect |
| 7. #350×C137 | C2 | semidirect |
| 14. C2×Dic548 | C22 | semidirect |
| 20. #17984024 | C22 | semidirect |
| 23. M32×C137 | C22 | semidirect |
| 24. C2×C16×C137 | C22 | semidirect |
| 91. C137 | #2194 | semidirect |
| 99. #350 | D137 | semidirect |
| 113. M32 | C2×D137 | semidirect |
| 114. C2×C16 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578208 | 2 |
| #22577846 | 2 |
| C2×#17984033 | 2 |
| #22577678 | 2 |
| #22577217 | 2 |
| #22577211 | 2 |
| #350×C137 | 2 |
| #2194 | 137 |