Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
398 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22569314 | C2 | semidirect |
| 3. #22558873 | C2 | semidirect |
| 5. #22558109 | C2 | semidirect |
| 6. #22558107 | C2 | semidirect |
| 156. C67 | #9008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570554 | 2 |
| #22569314 | 2 |
| #22558873 | 2 |
| #22558678 | 2 |
| #22558109 | 2 |
| #22558107 | 2 |
| C67×#1496 | 2 |
| #9008 | 67 |