Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
224 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #22558272 | C2 | semidirect |
| 4. Q8⋊(C67⋊C16) | C2 | semidirect |
| 6. #22558125 | C2 | semidirect |
| 7. Q8×C16×C67 | C2 | semidirect |
| 67. C16×C67 | SD16 | semidirect |
| 70. Q8×C67 | M32 | semidirect |
| 106. Q8×C16 | D67 | semidirect |
| 113. C67 | #12050 | semidirect |
| 173. C16 | #11761615 | semidirect |
| 176. Q8 | #14523982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562042 | 2 |
| C8×#11761615 | 2 |
| #22558272 | 2 |
| Q8⋊(C67⋊C16) | 2 |
| #22558163 | 2 |
| #22558125 | 2 |
| Q8×C16×C67 | 2 |
| #12050 | 67 |