Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
346 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
| 2. #22562244 | C2 | semidirect |
| 3. #22559564 | C2 | semidirect |
| 4. #22558264 | C2 | semidirect |
| 5. #22558170 | C2 | semidirect |
| 6. D4⋊(C67⋊C16) | C2 | semidirect |
| 7. C67×#3334 | C2 | semidirect |
| 97. D4×C67 | D16 | semidirect |
| 144. #3334 | D67 | semidirect |
| 151. C67 | #12340 | semidirect |
| 246. D4 | #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 |
| #22559564 | 2 |
| #22558264 | 2 |
| #22558170 | 2 |
| D4⋊(C67⋊C16) | 2 |
| C67×#3334 | 2 |
| #12340 | 67 |