Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×#16863218 | C2 | semidirect |
| 4. #22560935 | C2 | semidirect |
| 5. #22558308 | C2 | semidirect |
| 6. #22558290 | C2 | semidirect |
| 18. #16863206 | C4 | semidirect |
| 87. Q16×C67 | C4⋊C4 | semidirect |
| 91. D8×C67 | C4⋊C4 | semidirect |
| 164. C67 | #12950 | semidirect |
| 229. Q16 | Dic67⋊C4 | semidirect |
| 233. D8 | Dic67⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863513 | 2 |
| C2×#16863218 | 2 |
| C2×#16863206 | 2 |
| #22560935 | 2 |
| #22558308 | 2 |
| #22558290 | 2 |
| C2×#360×C67 | 2 |
| #12950 | 67 |