Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
530 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 135 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. #22561038 | C2 | semidirect |
| 2. C4×#14523953 | C2 | semidirect |
| 3. #22558965 | C2 | semidirect |
| 4. #22558660 | C2 | semidirect |
| 14. #500×C67 | C4 | semidirect |
| 15. #493×C67 | C4 | semidirect |
| 16. #486×C67 | C4 | semidirect |
| 101. C8×C67 | #104 | semidirect |
| 130. C67 | #9849 | semidirect |
| 132. #500 | Dic67 | semidirect |
| 133. #493 | Dic67 | semidirect |
| 134. #486 | Dic67 | semidirect |
| 228. C8 | #14523970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561038 | 2 |
| C4×#14523953 | 2 |
| #22558965 | 2 |
| #22558660 | 2 |
| C67×#3169 | 2 |
| #9849 | 67 |