Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22562361 | C2 | semidirect |
| 3. #22559727 | C2 | semidirect |
| 5. #22558191 | C2 | semidirect |
| 6. #22558179 | C2 | semidirect |
| 150. C67 | #12391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562445 | 2 |
| #22562361 | 2 |
| #22559727 | 2 |
| #22558252 | 2 |
| #22558191 | 2 |
| #22558179 | 2 |
| C67×#3402 | 2 |
| #12391 | 67 |