Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
224 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 87 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. Q8×C67⋊C16 | C2 | semidirect |
| 4. #22558272 | C2 | semidirect |
| 6. #22558125 | C2 | semidirect |
| 7. C67×Q8⋊C16 | C2 | semidirect |
| 57. C67⋊C16 | SD16 | semidirect |
| 70. Q8×C67 | M32 | semidirect |
| 110. Q8⋊C16 | D67 | semidirect |
| 113. C67 | #12050 | semidirect |
| 176. Q8 | #14523982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C67⋊C16 | 2 |
| #22562040 | 2 |
| C8×#11761615 | 2 |
| #22558272 | 2 |
| #22558165 | 2 |
| #22558125 | 2 |
| C67×Q8⋊C16 | 2 |
| #12050 | 67 |