Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
224 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 74 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. #22578459 | C2 | semidirect |
| 2. C2×#17984161 | C2 | semidirect |
| 3. #22578302 | C2 | semidirect |
| 4. #22578301 | C2 | semidirect |
| 7. #17984162 | C22 | semidirect |
| 11. C2×#14555513 | C22 | semidirect |
| 101. D137 | #350 | semidirect |
| 102. C137 | C2×#350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578459 | 2 |
| C2×#17984161 | 2 |
| #22578302 | 2 |
| #22578301 | 2 |
| #131×D137 | 2 |
| C2×#350 | 137 |