Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1350 conjugacy classes of subgroups; only the 367 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 367 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×#16863461 | C2 | semidirect |
| 3. #22561002 | C2 | semidirect |
| 4. C42×C67⋊C8 | C2 | semidirect |
| 5. C67×#1842 | C2 | semidirect |
| 22. #14524040 | C8 | semidirect |
| 29. C4×C67⋊C8 | D4 | semidirect |
| 38. C2×D268 | C2×C8 | semidirect |
| 53. C42×C67 | C2×C8 | semidirect |
| 73. C67⋊C8 | #127 | semidirect |
| 81. C4×C67 | C8×D4 | semidirect |
| 93. #1842 | D67 | semidirect |
| 95. C67 | C8×#127 | semidirect |
| 143. C42 | C8×D67 | semidirect |
| 172. C4 | #16863461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863461 | 2 |
| C4×#14524040 | 2 |
| #22561002 | 2 |
| C42×C67⋊C8 | 2 |
| C67×#1842 | 2 |
| C8×#127 | 67 |