Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
214 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 97 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×C32×D67 | C2 | semidirect |
| 3. (C2×D67)⋊C32 | C2 | semidirect |
| 4. C4×C67⋊C32 | C2 | semidirect |
| 5. C67×C4⋊C32 | C2 | semidirect |
| 23. C67⋊C32 | D4 | semidirect |
| 47. D268 | C32 | semidirect |
| 57. C2×D67 | C2×C32 | semidirect |
| 59. C4×C67 | C2×C32 | semidirect |
| 70. C4⋊C32 | D67 | semidirect |
| 73. C67 | D4×C32 | semidirect |
| 128. C4 | C32×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D67 | 2 |
| C16×D268 | 2 |
| (C2×D67)⋊C32 | 2 |
| C4×C67⋊C32 | 2 |
| C67×C4⋊C32 | 2 |
| D4×C32 | 67 |