Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
288 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22558287 | C2 | semidirect |
| 29. C2×D4×C67 | C16 | semidirect |
| 100. C67 | #7102 | semidirect |
| 126. C2×D4 | C67⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22558287 | 2 |
| C67×#1954 | 2 |
| #7102 | 67 |