Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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. #22578413 | C2 | semidirect |
| 3. #22578271 | C2 | semidirect |
| 13. C2×#14555494 | C4 | semidirect |
| 14. C2×#14555493 | C4 | semidirect |
| 16. C2×C8×D137 | C4 | semidirect |
| 18. C22×C8×C137 | C4 | semidirect |
| 85. C137 | #1812 | semidirect |
| 99. C22×C8 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578413 | 2 |
| #22578382 | 2 |
| #22578271 | 2 |
| C2×#17984094 | 2 |
| #1812 | 137 |