Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
256 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 11. C4⋊#11764040 | C4 | semidirect |
| 70. C4×C137 | #107 | semidirect |
| 83. C137 | #1947 | semidirect |
| 155. C4 | #17984021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984021 | 2 |
| C2×C4⋊#11764040 | 2 |
| #22577273 | 2 |
| #22577165 | 2 |
| C4×C4⋊C4×C137 | 2 |
| #1947 | 137 |