Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
272 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 9. C4⋊#11764040 | C4 | semidirect |
| 15. C4×C8×C137 | C4 | semidirect |
| 50. C8×C137 | C4⋊C4 | semidirect |
| 57. C4×C137 | #97 | semidirect |
| 68. C137 | #1770 | semidirect |
| 83. C4×C8 | Dic137 | semidirect |
| 119. C8 | C4⋊Dic137 | semidirect |
| 127. C4 | #17983998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11764040 | 2 |
| C2×#17983998 | 2 |
| C4×C4⋊Dic137 | 2 |
| #22577157 | 2 |
| C2×C4×C8×C137 | 2 |
| #1770 | 137 |