Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
228 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 11. C4⋊Q8×C137 | C4 | semidirect |
| 12. C4⋊Q8×C137 | C4 | semidirect |
| 17. C4×Q8×C137 | C4 | semidirect |
| 75. C137 | #1506 | semidirect |
| 81. C4⋊Q8 | Dic137 | semidirect |
| 82. C4⋊Q8 | Dic137 | semidirect |
| 87. C4×Q8 | Dic137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577460 | 2 |
| #22577249 | 2 |
| #22577140 | 2 |
| #533×C137 | 2 |
| #1506 | 137 |