Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
834 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 147 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. C2×#16863122 | C2 | semidirect |
| 2. #22558141 | C2 | direct (N × H) |
| 6. #16863122 | C22 | semidirect |
| 23. C22×D4×C67 | C8 | semidirect |
| 59. C2×D4×C67 | C2×C8 | semidirect |
| 159. C2×C67 | #1318 | semidirect |
| 166. C67 | C2×#1318 | semidirect |
| 183. C22×D4 | C67⋊C8 | semidirect |
| 220. C2×D4 | C2×C67⋊C8 | semidirect |
| 321. C2 | #22558141 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863122 | 2 |
| #22558141 | 2 |
| C2×#390×C67 | 2 |
| C2×#1318 | 67 |