Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
224 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 64 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×#17984161 | C2 | semidirect |
| 2. D137⋊#108 | C2 | semidirect |
| 3. #22578318 | C2 | semidirect |
| 4. #22578317 | C2 | semidirect |
| 8. #17984161 | C22 | semidirect |
| 10. #17984159 | C22 | semidirect |
| 100. D137 | #359 | semidirect |
| 101. C137 | C2×#359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984161 | 2 |
| D137⋊#108 | 2 |
| #22578318 | 2 |
| #22578317 | 2 |
| #135×D137 | 2 |
| C2×#359 | 137 |