Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
504 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22558547 | C2 | semidirect |
| 3. #22558152 | C2 | semidirect |
| 4. #22558140 | C2 | semidirect |
| 5. C67×#1465 | C2 | semidirect |
| 62. C2×D268 | M16 | semidirect |
| 86. C4×Dic67 | M16 | semidirect |
| 207. #1465 | D67 | semidirect |
| 210. C67 | #11533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562931 | 2 |
| #22558547 | 2 |
| #22558152 | 2 |
| #22558140 | 2 |
| C67×#1465 | 2 |
| #11533 | 67 |