Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
400 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 129 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×#17984017 | C2 | semidirect |
| 4. #22577158 | C2 | semidirect |
| 5. #336×C137 | C2 | semidirect |
| 29. C2×C4×D137 | C8 | semidirect |
| 91. C2×D137 | C4⋊C8 | semidirect |
| 98. Dic137 | C22⋊C8 | semidirect |
| 107. C137 | #1797 | semidirect |
| 113. #336 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D137 | 2 |
| C2×#17984017 | 2 |
| C2×#17984000 | 2 |
| #22577158 | 2 |
| #336×C137 | 2 |
| #1797 | 137 |