Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
314 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22572602 | C2 | semidirect |
| 2. #22562433 | C2 | semidirect |
| 3. #22562250 | C2 | semidirect |
| 5. #22558266 | C2 | semidirect |
| 6. #22558174 | C2 | semidirect |
| 7. C67×D4⋊C16 | C2 | semidirect |
| 89. D4×C67 | SD32 | semidirect |
| 141. D4⋊C16 | D67 | semidirect |
| 142. C67 | #12342 | semidirect |
| 232. D4 | #14523988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22572602 | 2 |
| #22562433 | 2 |
| #22562250 | 2 |
| #22559564 | 2 |
| #22558266 | 2 |
| #22558174 | 2 |
| C67×D4⋊C16 | 2 |
| #12342 | 67 |