Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
234 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22559827 | C2 | semidirect |
| 3. #22558279 | C2 | semidirect |
| 4. #22558265 | C2 | semidirect |
| 43. D8×C67 | Q16 | semidirect |
| 94. C67 | #12445 | semidirect |
| 129. D8 | Dic268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562346 | 2 |
| #22559827 | 2 |
| #22558279 | 2 |
| #22558265 | 2 |
| C8×D8×C67 | 2 |
| #12445 | 67 |