Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
126 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 22. #14555522 | Q8 | semidirect |
| 59. C137 | #2183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578506 | 2 |
| C4⋊#14555522 | 2 |
| #22578497 | 2 |
| C4×#14555522 | 2 |
| #22578452 | 2 |
| #2183 | 137 |