Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22559119 | C2 | semidirect |
| 4. #22558275 | C2 | semidirect |
| 5. #22558180 | C2 | semidirect |
| 7. C67×#1313 | C2 | semidirect |
| 109. #1313 | D67 | semidirect |
| 110. C67 | #12077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562075 | 2 |
| #22559119 | 2 |
| #22559034 | 2 |
| #22558275 | 2 |
| #22558180 | 2 |
| #22558177 | 2 |
| C67×#1313 | 2 |
| #12077 | 67 |