Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
236 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22562042 | C2 | semidirect |
| 3. #22558272 | C2 | semidirect |
| 4. D4⋊(C67⋊C16) | C2 | semidirect |
| 5. #22558163 | C2 | semidirect |
| 6. #22558128 | C2 | semidirect |
| 7. C67×#2169 | C2 | semidirect |
| 93. C67⋊C8 | M32 | semidirect |
| 115. #2169 | D67 | semidirect |
| 121. C67 | #12064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562042 | 2 |
| C8×#11761613 | 2 |
| #22558272 | 2 |
| D4⋊(C67⋊C16) | 2 |
| #22558163 | 2 |
| #22558128 | 2 |
| C67×#2169 | 2 |
| #12064 | 67 |