Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
520 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22573343 | C2 | semidirect |
| 2. #22569929 | C2 | semidirect |
| 3. C2×#16863203 | C2 | semidirect |
| 4. C2×#16863202 | C2 | semidirect |
| 5. #22561823 | C2 | semidirect |
| 6. #22558312 | C2 | semidirect |
| 7. C67×#3067 | C2 | semidirect |
| 225. #3067 | D67 | semidirect |
| 230. C67 | #13312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573343 | 2 |
| #22569929 | 2 |
| C2×#16863203 | 2 |
| C2×#16863202 | 2 |
| #22561823 | 2 |
| #22558312 | 2 |
| C67×#3067 | 2 |
| #13312 | 67 |