Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 8. C2×#14555513 | C4 | semidirect |
| 12. #17984028 | C4 | semidirect |
| 15. M32×C137 | C4 | semidirect |
| 58. C137 | #1379 | semidirect |
| 68. M32 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984161 | 2 |
| #22578366 | 2 |
| M32×D137 | 2 |
| #1379 | 137 |