Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
396 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 18. #16863200 | C4 | semidirect |
| 143. C67 | #12957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863503 | 2 |
| C2×#16863220 | 2 |
| #22561929 | 2 |
| #22560960 | 2 |
| #22558315 | 2 |
| #22558288 | 2 |
| C2×#362×C67 | 2 |
| #12957 | 67 |