Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
258 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 8. #16863174 | C4 | semidirect |
| 15. #346×C67 | C4 | semidirect |
| 16. C4×C16×C67 | C4 | semidirect |
| 83. C67 | #12597 | semidirect |
| 90. #346 | Dic67 | semidirect |
| 91. C4×C16 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561814 | 2 |
| #22559964 | 2 |
| #22558297 | 2 |
| #22558294 | 2 |
| C67×#2108 | 2 |
| #12597 | 67 |