Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22577844 | C2 | direct (N × H) |
| 3. C2×#17984034 | C2 | semidirect |
| 4. C2×#17984031 | C2 | semidirect |
| 5. C2×#17984028 | C2 | semidirect |
| 6. C22×Q16×C137 | C2 | semidirect |
| 13. #17984034 | C22 | semidirect |
| 14. #17984031 | C22 | semidirect |
| 15. #17984028 | C22 | semidirect |
| 21. C2×Q16×C137 | C22 | semidirect |
| 80. C2×C137 | #510 | semidirect |
| 83. C137 | C2×#510 | semidirect |
| 86. C22×Q16 | D137 | semidirect |
| 99. C2×Q16 | C2×D137 | semidirect |
| 165. C2 | #22577844 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984110 | 2 |
| #22577844 | 2 |
| C2×#17984034 | 2 |
| C2×#17984031 | 2 |
| C2×#17984028 | 2 |
| C22×Q16×C137 | 2 |
| C2×#510 | 137 |