Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
252 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 252 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. #22562464 | C2 | semidirect |
| 2. D4×C67⋊C16 | C2 | semidirect |
| 3. #22559574 | C2 | semidirect |
| 4. #22558282 | C2 | semidirect |
| 5. #22558257 | C2 | semidirect |
| 6. #22558255 | C2 | semidirect |
| 55. C67⋊C16 | D8 | semidirect |
| 82. D4×C67 | SD32 | semidirect |
| 125. C67 | #12432 | semidirect |
| 202. D4 | #14523987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562464 | 2 |
| D4×C67⋊C16 | 2 |
| #22559574 | 2 |
| #22558282 | 2 |
| #22558257 | 2 |
| #22558255 | 2 |
| C67×#1667 | 2 |
| #12432 | 67 |