Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
158 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 1. C2×#17984034 | C2 | semidirect |
| 4. C4⋊#14555485 | C2 | semidirect |
| 5. #22577206 | C2 | semidirect |
| 7. C4×Q16×C137 | C2 | semidirect |
| 72. C137 | #2211 | semidirect |
| 77. C4×Q16 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984034 | 2 |
| C2×#17984031 | 2 |
| #22577787 | 2 |
| C4⋊#14555485 | 2 |
| #22577206 | 2 |
| #22577203 | 2 |
| C4×Q16×C137 | 2 |
| #2211 | 137 |