Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22561187 | C2 | semidirect |
| 3. #22560325 | C2 | semidirect |
| 4. #22558899 | C2 | semidirect |
| 6. #22558084 | C2 | semidirect |
| 84. C4×Dic67 | SD16 | semidirect |
| 197. C67 | #10521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561187 | 2 |
| #22561038 | 2 |
| #22560325 | 2 |
| #22558899 | 2 |
| #22558886 | 2 |
| #22558084 | 2 |
| C67×#3246 | 2 |
| #10521 | 67 |