Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
396 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 15. #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×#16863218 | 2 |
| C2×#16863212 | 2 |
| #22561929 | 2 |
| #22560962 | 2 |
| #22558316 | 2 |
| #22558289 | 2 |
| C2×#441×C67 | 2 |
| #12957 | 67 |