Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
480 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22561350 | C2 | semidirect |
| 3. #22561308 | C2 | semidirect |
| 4. #22558035 | C2 | semidirect |
| 5. #22558035 | C2 | semidirect |
| 94. C2×D4×C67 | Q16 | semidirect |
| 212. C67 | #7782 | semidirect |
| 284. C2×D4 | #11761618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561350 | 2 |
| #22561345 | 2 |
| #22561308 | 2 |
| #22558035 | 2 |
| #22558030 | 2 |
| C67×#2804 | 2 |
| #7782 | 67 |