Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1350 conjugacy classes of subgroups; only the 447 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 447 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×D4×C67⋊C8 | C2 | semidirect |
| 2. #22561004 | C2 | semidirect |
| 3. #22560361 | C2 | semidirect |
| 4. C42×C67⋊C8 | C2 | semidirect |
| 24. C4×C67⋊C8 | D4 | semidirect |
| 27. #127×C67 | C8 | semidirect |
| 43. C2×D4×C67 | C2×C8 | semidirect |
| 53. C42×C67 | C2×C8 | semidirect |
| 73. C67⋊C8 | #127 | direct (N × H) |
| 82. C4×C67 | C8×D4 | semidirect |
| 95. C67 | C8×#127 | semidirect |
| 113. #127 | C67⋊C8 | direct (N × H) |
| 128. C2×D4 | C2×C67⋊C8 | semidirect |
| 143. C42 | C2×C67⋊C8 | semidirect |
| 172. C4 | D4×C67⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C67⋊C8 | 2 |
| #22561004 | 2 |
| #22560361 | 2 |
| C42×C67⋊C8 | 2 |
| C4×#127×C67 | 2 |
| C8×#127 | 67 |