Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
278 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#17984023 | C2 | semidirect |
| 5. #22577168 | C2 | semidirect |
| 6. #22577167 | C2 | semidirect |
| 7. C2×#108×C137 | C2 | semidirect |
| 99. C2×D137 | #108 | semidirect |
| 113. C137 | #1855 | semidirect |
| 117. C2×#108 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D137 | 2 |
| C2×#17984023 | 2 |
| #22577366 | 2 |
| C2×#17984000 | 2 |
| #22577168 | 2 |
| #22577167 | 2 |
| C2×#108×C137 | 2 |
| #1855 | 137 |