Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
598 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22570669 | C2 | semidirect |
| 2. #22566149 | C2 | semidirect |
| 3. #22558934 | C2 | semidirect |
| 4. #22558807 | C2 | semidirect |
| 5. #22558717 | C2 | semidirect |
| 6. #22558101 | C2 | semidirect |
| 198. C67 | #10090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570669 | 2 |
| #22566149 | 2 |
| #22558934 | 2 |
| #22558807 | 2 |
| #22558717 | 2 |
| #22558101 | 2 |
| C67×#3213 | 2 |
| #10090 | 67 |