Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22562465 | C2 | semidirect |
| 2. #22559827 | C2 | semidirect |
| 4. C8×C16×C67 | C2 | semidirect |
| 32. C16×C67 | D8 | semidirect |
| 40. C8×C67 | SD32 | semidirect |
| 55. C8×C16 | D67 | semidirect |
| 56. C67 | #12517 | semidirect |
| 84. C16 | D536 | semidirect |
| 92. C8 | #14523988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562465 | 2 |
| #22559827 | 2 |
| #22559824 | 2 |
| C8×C16×C67 | 2 |
| #12517 | 67 |