Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22562434 | C2 | semidirect |
| 3. #22559569 | C2 | semidirect |
| 4. #22558264 | C2 | semidirect |
| 5. Q8⋊(C67⋊C16) | C2 | semidirect |
| 6. #22558170 | C2 | semidirect |
| 7. Q8×D8×C67 | C2 | semidirect |
| 72. D8×C67 | SD16 | semidirect |
| 92. Q8×C67 | D16 | semidirect |
| 137. Q8×D8 | D67 | semidirect |
| 144. C67 | #12352 | semidirect |
| 206. D8 | #11761615 | semidirect |
| 229. Q8 | #14523984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562434 | 2 |
| #22562244 | 2 |
| #22559569 | 2 |
| #22558264 | 2 |
| Q8⋊(C67⋊C16) | 2 |
| #22558170 | 2 |
| Q8×D8×C67 | 2 |
| #12352 | 67 |