Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 29. C2×Dic268 | Q8 | semidirect |
| 148. C67 | #13368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570732 | 2 |
| #22561930 | 2 |
| #22561928 | 2 |
| #22561078 | 2 |
| #22558316 | 2 |
| #22558292 | 2 |
| C67×#1386 | 2 |
| #13368 | 67 |