Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
238 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 99 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. Q16×C67⋊C8 | C2 | semidirect |
| 3. #22558281 | C2 | semidirect |
| 4. #22558173 | C2 | semidirect |
| 6. #22558125 | C2 | semidirect |
| 36. SD32×C67 | C8 | semidirect |
| 55. Q16×C67 | C2×C8 | semidirect |
| 67. C16×C67 | C2×C8 | semidirect |
| 113. C67 | #12043 | semidirect |
| 134. SD32 | C67⋊C8 | semidirect |
| 154. Q16 | C2×C67⋊C8 | semidirect |
| 173. C16 | C2×C67⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×C67⋊C8 | 2 |
| D8×C67⋊C8 | 2 |
| #22558281 | 2 |
| #22558173 | 2 |
| #22558170 | 2 |
| #22558125 | 2 |
| C4×SD32×C67 | 2 |
| #12043 | 67 |