Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
490 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #22560673 | C2 | semidirect |
| 2. #22560648 | C2 | semidirect |
| 3. #22560413 | C2 | semidirect |
| 4. #22558777 | C2 | semidirect |
| 5. #22558569 | C2 | semidirect |
| 6. #22558114 | C2 | semidirect |
| 232. C67 | #10560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22560673 | 2 |
| #22560648 | 2 |
| #22560413 | 2 |
| #22558777 | 2 |
| #22558569 | 2 |
| #22558114 | 2 |
| C67×#3192 | 2 |
| #10560 | 67 |