Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
372 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22558968 | C2 | semidirect |
| 3. #22558174 | C2 | semidirect |
| 4. #22558171 | C2 | semidirect |
| 5. C67×#2162 | C2 | semidirect |
| 65. Dic268 | M16 | semidirect |
| 68. D536 | M16 | semidirect |
| 152. #2162 | D67 | semidirect |
| 156. C67 | #11660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14524065 | 2 |
| #22558968 | 2 |
| #22558174 | 2 |
| #22558171 | 2 |
| C67×#2162 | 2 |
| #11660 | 67 |