Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
706 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 3. #22559826 | C2 | semidirect |
| 4. #22559818 | C2 | semidirect |
| 5. #22559804 | C2 | semidirect |
| 69. C2×C8×C67 | Q16 | semidirect |
| 115. C67 | #19604 | semidirect |
| 172. C2×C8 | #11761618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570791 | 2 |
| #22570723 | 2 |
| #22559826 | 2 |
| #22559818 | 2 |
| #22559804 | 2 |
| C2×C8×C67⋊C8 | 2 |
| C67×#3160 | 2 |
| #19604 | 67 |