Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
170 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22562486 | C2 | semidirect |
| 3. #22558408 | C2 | semidirect |
| 4. Dic67⋊C32 | C2 | semidirect |
| 7. C67×#1424 | C2 | semidirect |
| 81. #1424 | D67 | semidirect |
| 86. C67 | #13707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562486 | 2 |
| #22562055 | 2 |
| #22558408 | 2 |
| Dic67⋊C32 | 2 |
| #22558388 | 2 |
| #22558386 | 2 |
| C67×#1424 | 2 |
| #13707 | 67 |